trigonometry case study questions class 10 chapter 9

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Case Study Questions for Class 10 Maths Chapter 9 Applications of Trigonometry

• Last modified on: 1 year ago
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In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies as well. In that, a paragraph will be given, and then the MCQ questions or subjective questions based on it will be asked.

Here, we have provided case based/passage-based questions for Class 10 Maths Chapter 9 Applications of Trigonometry

Case Study Questions:

Question 1:

A Satellite flying at height h is watching the top of the two tallest mountains in Uttarakhand and Karnataka, them being Nanda Devi (height 7,816m) and Mullayanagiri (height 1,930 m). The angles of depression from the satellite to the top of Nanda Devi and Mullayanagiri are 30° and 60° respectively. If the distance between the peaks of two mountains is 1937 km, and the satellite is vertically above the midpoint of the distance between the two mountains.

(i) The distance of the satellite from the top of Mullayanagiri is

(a) 1139.4 km

(b) 577.52 km

(c) 1937 km

(d) 1025.36 km

(ii) If a mile stone very far away from, makes 45 to the top of Mullanyangiri mountain. So, find the distance of this milestone form the mountain.

(a) 1118.327 km

(b) 566.976 km

(iii) The distance of the satellite from the ground is

(iv) The distance of the satellite from the top of Nanda Devi is

(v) What is the angle of elevation if a man is standing at a distance of 7816m from Nanda Devi?

Question 2:

A group of students of class X visited India Gate on an educational trip. The teacher and students had interest in history as well. The teacher narrated that India Gate, official name Delhi Memorial, originally called All-India War Memorial, monumental sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919.The teacher also said that India Gate, which is located at the eastern end of the Rajpath (formerly called the Kingsway), is about 138 feet (42 m) in height.

(i) What is the angle of elevation if they are standing at a distance of 42 m away from the monument? (a) 30° (b) 45° (c) 60° (d) 0°

(ii) They want to see the tower at an angle of 60°. So, they want to know the distance where they should stand and hence find the distance. (a) 25.24 m (b) 20.12 m (c) 42 m (d) 24.24 m

(iii) If the altitude of the Sun is at 60°, then the height of the vertical tower that will cast a shadow of length 20 m is (a) 20 √ 3 m (b) 20/ √ 3 m (c) 15/ √ 3 m (d) 15 √ 3 m

(iv) The ratio of the length of a rod and its shadow is 1 : 1. The angle of elevation of the Sun is (a) 30° (b) 45° (c) 60° (d) 90°

(v) The angle formed by the line of sight with the horizontal when the object viewed is below the horizontal level is (a) corresponding angle (b) angle of elevation (c) angle of depression (d) complete angle

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You may also like:

Chapter 1 Real Numbers Chapter 2 Polynomials Chapter 3 Pair of Linear Equations in Two Variables C hapter 4 Quadratic Equations Chapter 5 Arithmetic Progressions Chapter 6 Triangles Chapter 7 Coordinate Geometry Chapter 8 Introduction to Trigonometry Chapter 9 Some Applications of Trigonometry Chapter 10 Circles Chapter 11 Constructions Chapter 12 Areas Related to Circles Chapter 13 Surface Areas and Volumes Chapter 14 Statistics Chapter 15 Probability

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• CBSE Class 10

CBSE Class 10 Maths Chapter 9 Some Applications of Trigonometry Competency-Focused Practice Questions With Answer Key 2024-25: Free PDF Download

Cbse class 10 maths chapter 9 practice questions 2025: cbse class 10 students check the competency-based practice questions of mathematics for chapter 9 some applications of trigonometry. download the practice questions along with the answer key for 2025 examination. .

CBSE 2024-25 Competency Based Questions With Answers: The Central Board of Secondary Education (CBSE) has made available the competency-based practice questions for the major subjects for the students of class 10. Students can check the questions for Mathematics, Science and Social Science. The competency-based practice questions are for the academic session 2024-25 and are available on cbseacademic.nic.in. 

What are Competency-Based Practice Questions?

Competency-focused practice questions are questions designed specifically to test conceptual understanding and application of concepts. They aim to encourage students to practice learning by doing. The idea behind designing the competency-based questions is to develop higher order skills such as analysis, critical thinking and problem solving in students. 

CBSE Class 10 Maths Chapter 9 Competency Based-Questions 

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4. Students should solve the problems from CBSE Class 10 subject textbook to clear the concepts and strengthen understanding. While solving problems, students should make it a habit to show rough work clearly which will help them in the examination as well. 

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Case Study on Some Applications of Trigonometry Class 10 Maths PDF

The passage-based questions are commonly known as case study questions. Students looking for Case Study on Some Applications of Trigonometry Class 10 Maths can use this page to download the PDF file. 

The case study questions on Some Applications of Trigonometry are based on the CBSE Class 10 Maths Syllabus, and therefore, referring to the Some Applications of Trigonometry case study questions enable students to gain the appropriate knowledge and prepare better for the Class 10 Maths board examination. Continue reading to know how should students answer it and why it is essential to solve it, etc.

Case Study on Some Applications of Trigonometry Class 10 Maths with Solutions in PDF

Our experts have also kept in mind the challenges students may face while solving the case study on Some Applications of Trigonometry, therefore, they prepared a set of solutions along with the case study questions on Some Applications of Trigonometry.

The case study on Some Applications of Trigonometry Class 10 Maths with solutions in PDF helps students tackle questions that appear confusing or difficult to answer. The answers to the Some Applications of Trigonometry case study questions are very easy to grasp from the PDF - download links are given on this page.

Why Solve Some Applications of Trigonometry Case Study Questions on Class 10 Maths?

There are three major reasons why one should solve Some Applications of Trigonometry case study questions on Class 10 Maths - all those major reasons are discussed below:

• To Prepare for the Board Examination: For many years CBSE board is asking case-based questions to the Class 10 Maths students, therefore, it is important to solve Some Applications of Trigonometry Case study questions as it will help better prepare for the Class 10 board exam preparation.
• Develop Problem-Solving Skills: Class 10 Maths Some Applications of Trigonometry case study questions require students to analyze a given situation, identify the key issues, and apply relevant concepts to find out a solution. This can help CBSE Class 10 students develop their problem-solving skills, which are essential for success in any profession rather than Class 10 board exam preparation.
• Understand Real-Life Applications: Several Some Applications of Trigonometry Class 10 Maths Case Study questions are linked with real-life applications, therefore, solving them enables students to gain the theoretical knowledge of Some Applications of Trigonometry as well as real-life implications of those learnings too.

How to Answer Case Study Questions on Some Applications of Trigonometry?

Students can choose their own way to answer Case Study on Some Applications of Trigonometry Class 10 Maths, however, we believe following these three steps would help a lot in answering Class 10 Maths Some Applications of Trigonometry Case Study questions.

• Read Question Properly: Many make mistakes in the first step which is not reading the questions properly, therefore, it is important to read the question properly and answer questions accordingly.
• Highlight Important Points Discussed in the Clause: While reading the paragraph, highlight the important points discussed as it will help you save your time and answer Some Applications of Trigonometry questions quickly.
• Go Through Each Question One-By-One: Ideally, going through each question gradually is advised so, that a sync between each question and the answer can be maintained. When you are solving Some Applications of Trigonometry Class 10 Maths case study questions make sure you are approaching each question in a step-wise manner.

What to Know to Solve Case Study Questions on Class 10 Some Applications of Trigonometry?

 A few essential things to know to solve Case Study Questions on Class 10 Some Applications of Trigonometry are -

• Basic Formulas of Some Applications of Trigonometry: One of the most important things to know to solve Case Study Questions on Class 10 Some Applications of Trigonometry is to learn about the basic formulas or revise them before solving the case-based questions on Some Applications of Trigonometry.
• To Think Analytically: Analytical thinkers have the ability to detect patterns and that is why it is an essential skill to learn to solve the CBSE Class 10 Maths Some Applications of Trigonometry case study questions.
• Strong Command of Calculations: Another important thing to do is to build a strong command of calculations especially, mental Maths calculations.

Where to Find Case Study on Some Applications of Trigonometry Class 10 Maths?

Use Selfstudys.com to find Case Study on Some Applications of Trigonometry Class 10 Maths. For ease, here is a step-wise procedure to download the Some Applications of Trigonometry Case Study for Class 10 Maths in PDF for free of cost.

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Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°.

Q. Write the value of sec 30°.

A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°.

horizontal line

Vertical line

Line of sight

Parallel lines

Let the speed of car be v m/s.

Let car takes t seconds to reach the point B from the point D

Distance travel by car in t sec = vt m.

In ΔABD, we have

h = √3 vt ...(i)

and in right D ABC, we have

Q. Write the value of cosec 60°.

Q. If the two lines are parallel; then the alternate opposite angles are ..................... .

None of these

Form a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and angle of elevation of the top of the flagstaff from P is 45°.

Q. What is the value of tan 45°?

AP = 10 √3 m

In right ΔPAD,

10 √3 = 10 + BD

BD = 10 √3 – 10

BD = 7.32 m.

BP 2 = AB 2 + AP 2

AB 2 = AP 2 + BP 2

AP 2 = AB 2 + BP 2

None of these.

From a point on the bridge across a river the angle of depression of the banks on opposite sides of the river 30° and 45° respectively.

Acute angled triangle

Right angled triangle

Obtuse angled triangle

Equilateral triangle.

From a point on the bridge across a river the angle of depression of the banks on opposite sides of the river 30° and 45° respectively.

Q. The value of tan 45° is

The value of tan 45° is = 1

1(√3 + 1) m

3(√3 + 1) m

In ΔPDB, ∠B = 45°

tan 45° = PD/DB

width of the river = AB = AD + DB

= 3(√3 + 1)m.

Perpendicular/Base

Base/Perpendicular

Hypotenuse/Base

Perpendicular/Hypotenuse

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Case Based Questions: Some Application of Trigonometry Free PDF Download

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CBSE Class 10 Maths Case Study Questions PDF

Download Case Study Questions for Class 10 Mathematics to prepare for the upcoming CBSE Class 10 Final Exam. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 10 so that they can score 100% on Boards.

CBSE Class 10 Mathematics Exam 2024  will have a set of questions based on case studies in the form of MCQs. The CBSE Class 10 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.

Table of Contents

Chapterwise Case Study Questions for Class 10 Mathematics

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

The above  Case studies for Class 10 Maths will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 10 Mathematics Case Studies have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

• Class 10th Science Case Study Questions
• Assertion and Reason Questions of Class 10th Science
• Assertion and Reason Questions of Class 10th Social Science

Class 10 Maths Syllabus 2024

Chapter-1  real numbers.

Starting with an introduction to real numbers, properties of real numbers, Euclid’s division lemma, fundamentals of arithmetic, Euclid’s division algorithm, revisiting irrational numbers, revisiting rational numbers and their decimal expansions followed by a bunch of problems for a thorough and better understanding.

Chapter-2  Polynomials

This chapter is quite important and marks securing topics in the syllabus. As this chapter is repeated almost every year, students find this a very easy and simple subject to understand. Topics like the geometrical meaning of the zeroes of a polynomial, the relationship between zeroes and coefficients of a polynomial, division algorithm for polynomials followed with exercises and solved examples for thorough understanding.

Chapter-3  Pair of Linear Equations in Two Variables

This chapter is very intriguing and the topics covered here are explained very clearly and perfectly using examples and exercises for each topic. Starting with the introduction, pair of linear equations in two variables, graphical method of solution of a pair of linear equations, algebraic methods of solving a pair of linear equations, substitution method, elimination method, cross-multiplication method, equations reducible to a pair of linear equations in two variables, etc are a few topics that are discussed in this chapter.

Chapter-4  Quadratic Equations

The Quadratic Equations chapter is a very important and high priority subject in terms of examination, and securing as well as the problems are very simple and easy. Problems like finding the value of X from a given equation, comparing and solving two equations to find X, Y values, proving the given equation is quadratic or not by knowing the highest power, from the given statement deriving the required quadratic equation, etc are few topics covered in this chapter and also an ample set of problems are provided for better practice purposes.

Chapter-5  Arithmetic Progressions

This chapter is another interesting and simpler topic where the problems here are mostly based on a single formula and the rest are derivations of the original one. Beginning with a basic brief introduction, definitions of arithmetic progressions, nth term of an AP, the sum of first n terms of an AP are a few important and priority topics covered under this chapter. Apart from that, there are many problems and exercises followed with each topic for good understanding.

Chapter-6  Triangles

This chapter Triangle is an interesting and easy chapter and students often like this very much and a securing unit as well. Here beginning with the introduction to triangles followed by other topics like similar figures, the similarity of triangles, criteria for similarity of triangles, areas of similar triangles, Pythagoras theorem, along with a page summary for revision purposes are discussed in this chapter with examples and exercises for practice purposes.

Chapter-7  Coordinate Geometry

Here starting with a general introduction, distance formula, section formula, area of the triangle are a few topics covered in this chapter followed with examples and exercises for better and thorough practice purposes.

Chapter-8  Introduction to Trigonometry

As trigonometry is a very important and vast subject, this topic is divided into two parts where one chapter is Introduction to Trigonometry and another part is Applications of Trigonometry. This Introduction to Trigonometry chapter is started with a general introduction, trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles, trigonometric identities, etc are a few important topics covered in this chapter.

Chapter-9  Applications of Trigonometry

This chapter is the continuation of the previous chapter, where the various modeled applications are discussed here with examples and exercises for better understanding. Topics like heights and distances are covered here and at the end, a summary is provided with all the important and frequently used formulas used in this chapter for solving the problems.

Chapter-10  Circle

Beginning with the introduction to circles, tangent to a circle, several tangents from a point on a circle are some of the important topics covered in this chapter. This chapter being practical, there are an ample number of problems and solved examples for better understanding and practice purposes.

Chapter-11  Constructions

This chapter has more practical problems than theory-based definitions. Beginning with a general introduction to constructions, tools used, etc, the topics like division of a line segment, construction of tangents to a circle, and followed with few solved examples that help in solving the exercises provided after each topic.

Chapter-12  Areas related to Circles

This chapter problem is exclusively formula based wherein topics like perimeter and area of a circle- A Review, areas of sector and segment of a circle, areas of combinations of plane figures, and a page summary is provided just as a revision of the topics and formulas covered in the entire chapter and also there are many exercises and solved examples for practice purposes.

Chapter-13  Surface Areas and Volumes

Starting with the introduction, the surface area of a combination of solids, the volume of a combination of solids, conversion of solid from one shape to another, frustum of a cone, etc are to name a few topics explained in detail provided with a set of examples for a better comprehension of the concepts.

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Probability is another simple and important chapter in examination point of view and as seeking knowledge purposes as well. Beginning with an introduction to probability, an important topic called A theoretical approach is explained here. Since this chapter is one of the smallest in the syllabus and problems are also quite easy, students often like this chapter

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Case Study Questions Class 10 Maths Some Applications of Trigonometry

Case study questions class 10 maths chapter 9 some applications of trigonometry.

CBSE Class 10 Case Study Questions Maths Some Applications of Trigonometry. Term 2 Important Case Study Questions for Class 10 Board Exam Students. Here we have arranged some Important Case Base Questions for students who are searching for Paragraph Based Questions Some Applications of Trigonometry.

CBSE Case Study Questions Class 10 Maths Some Applications of Trigonometry

Case Study – 1

[KVS Raipur 2021 – 22]

Answer – 20√3m

Answer – a) corresponding angle 

[ CBSE Academic Question Paper ]

(a) 1139.4 km

(d) 1025.36 km

Answer: (c) 1937 km

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CBSE Case Study Questions for Class 10 Maths Trigonometry Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Trigonometry  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

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• Chapter 10 Circles Case Study Questions

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Important Questions for Class 10 Maths Chapter 9 Some Applications of Trigonometry

August 7, 2019 by Sastry CBSE

Some Applications of Trigonometry Class 10 Important Questions Very Short Answer (1 Mark)

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Some Applications of Trigonometry Class 10 Important Questions Long Answer (4 Marks)

Question 33. The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building. (2013OD) Solution: Refer to Question 30, Page 143.

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Important Questions for Class 10 Maths Chapter 9 - Some Applications of Trigonometry

• Class 10 Important Question
• Chapter 9: Some Applications Of Trigonometry

CBSE Class 10 Maths Important Questions Chapter 9 - Some Applications of Trigonometry - Free PDF Download

Trigonometry is always an important concept in mathematics. Although some may find it a complicated topic, once the basics are straightforward, it is very easy to tackle various levels. Moreover, practising is the best tool for any math concept, the same as trigonometry. Applications of trigonometry can be seen in many daily life cases. Furthermore, it is a very scoring topic for board exams too. Class 10 Maths Chapter 9 is an important topic from the exam point of view. Good capture of this topic will help you score good marks from the exam point of view.

Vedantu is a platform that provides free CBSE Solutions and other study materials for students. Students can register and get access to the best and reliable source of study materials specially made by master teachers at Vedantu. You can Download Maths NCERT Solutions Class 10 to help you to revise the complete Syllabus and score more marks in your examinations. Subjects like Science, Maths, Engish will become easy to study if you have access to Class 10 Science NCERT Solutions , Maths solutions, and solutions of other subjects that are available on Vedantu only.

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Important Questions for CBSE Class 10 Maths Chapter 9 - Free PDF Download

Important questions for class 10 maths chapter 9 – Applications of Trigonometry are prepared with the vision to enable students to understand the essential topics of the chapter and study accordingly. Practising these questions can bring in-depth knowledge for students on the same subject. It is known that conceptual understanding has a pivotal role in maths. Students would be able to do questions only after they understand the concept in a clear cut manner. Moreover, practising these questions can give an excellent idea to understand which portions weigh more and know from where we have to expect questions for the board exam.

Applications of Trigonometry:

Applications of trigonometry chapter is a continuation of the previous chapter of trigonometry. Here we deal with applications of the concepts learned in the chapter trigonometry. We use the concepts of trigonometry learned during the last chapter to solve questions that include situations that we may face in our daily lives.

Suppose if you are standing near a tall building and you want to measure its height, or else suppose you are just standing on a bridge across a river and you want to measure a river's width. How can you measure the height of the building and the width of the river in both cases?

To measure the building's length, we have to go to the top of the building, drop a tall rope, and then measure the string's length. Calculating the width of the river can be more difficult as if we have to stand on both sides of the river with a long rope. These methods may seem weird for most of us as they do not seem practical. But once you are now trigonometry, the task will be easy.

Applications of trigonometry can very well be used to measure heights and distances too in an accurate manner. Trigonometry has several other applications. However, to get into the trigonometry applications, it is imperative to revise the basics of trigonometry.

Basics of Trigonometry

Trigonometric ratios form the basic step of each question from the topic. Trigonometric ratios are always derived from the sides of the right angle. Let us see some of the standard ratios used for applying trigonometry:

Sin = Perpendicular / Hypotenuse

Cos = Base / Hypotenuse

Tan = Perpendicular / Base 

Cosec = 1 / sin =Hypotenuse / Perpendicular

Sec = 1 / cos = Hypotenuse / Base

Cot = 1 / tan = Base / Perpendicular

To solve any question on heights and distances, the first and foremost thing is to draw a clean, neat, and friendly diagram labelling all the available angles and sides. The point of observation or measurement should also be included as a point in the triangle representing the question. Right angle or 90 degree is necessary to apply trigonometric ratios in such problems. The height, base, and hypotenuse should also be appropriately marked in the diagram to simplify it.

Line of Sight

Line of sight is a critical concept in trigonometry as it is based on the line of sight that angle of elevation and angle of depression is measured. When we look upon an object, an imaginary straight line connects our eyes, and the object is called the line of sight.

The angle of elevation is the angle made between the horizontal and our line of vision when we look up, and angle of depression is the angle between horizontal and the line of vision when we look down upon an object.

Besides the right angle or 90-degree angle, the angle of elevation and angle of depression plays a significant role in measuring the height of buildings or the height of any such things from an observer's point of view. Based on these angles, trigonometric ratios are applied, and the base and height are decided. If we look upon a building whose height is to be measured, the angle made is the angle of elevation, and if we are looking down for something whose depth is to be measured, the angle made is the angle of depression.

The unknown values which represent the height or distance to be measured are calculated in such a way by applying equations of trigonometric ratios to both known and unknown values. From it, the unknown is calculated. We must always take care that the unknown value should represent any one of the equation variables and apply trigonometric ratio, which includes that side. The unknown value may be based on, height or hypotenuse of the triangle. 

Practising Important Questions of Class 10 Maths Chapter 9- Applications of trigonometry are the ultimate method to tackle any kind of questions from the topic. As we say Practice makes a man perfect, the same is the case for trigonometry too. Once the basics are clear, students should go on solving NCERT questions and other important questions as well.

Practice Questions of Chapter 9

Some of the questions that can help students with their preparations for upcoming board examinations are mentioned below.

Find the height of the tower from 20m from the foot of the tower with an elevation angle of 30 degrees.

Answer: 11.56 m.

When a staircase is lying against a wall, it forms a 60° angle with the horizontal. Calculate the length of the ladder if the foot of the ladder is 2.5 metres from the wall.

Answer: 5 m

The angle of elevation of the top of a tower from a location 20 metres away is 30 degrees. Determine the tower's height.

Answer : 11.56 m

A flagstaff perches atop a 5m tall structure. The angle of elevation of the top of the flagstaff is 60 degrees from a point on earth, while the angle of elevation of the top of the structure is 45 degrees from the same point. Determine the flagstaff's height.

Answer:   3.65 m

The foot of a tower is reached along a straight highway. A man standing at the top of the tower notices a car approaching the foot of the tower at a consistent pace at a 30° angle of depression. The angle of dip of the automobile is found to be 60 degrees six seconds later. Calculate the time it took the car to go to the foot of the tower from this location.

Answer: 3 sec  

Solved Question and Answers

1. If sec 2A = cosec (A – 60°), where 4A is an acute angle, find the value of A.

Ans: A = 50°

2. Mahima is given the trigonometric ratio of tan θ = 5/12. How to find the trigonometric ratio of cosec θ using trigonometry formulas.

Ans: Using trigonometry formulas, cosec θ = 13/5

3. If sin θ cos θ = 5, find the value of (sin θ + cos θ) 2 using the trigonometry formulas.

Ans:  11

4. Find the exact value of sin 75° using the trigonometric identities.

Ans: Sin 75°= (√3 + 1)/2√2

5. Given 15 cot A = 8, find sin A and sec A

Ans: sin A = 15/17 and sec A = 17/8.

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Trigonometry is about understanding the relationships in right-angled triangles, especially the ratios of their sides called trigonometric ratios. The article above shares essential trigonometric formulas and introduces "Important Questions for Class 10 Maths Chapter 9 - Some Applications of Trigonometry." These questions help you apply trigonometry in real situations, making it easier to grasp. Connecting theory with practical examples, this resource becomes a handy guide, ensuring you get the hang of trigonometric concepts and their use in triangles. It's like a toolkit for tackling math problems related to triangles. 

Important Related Links for CBSE Class 10 Maths

FAQs on Important Questions for Class 10 Maths Chapter 9 - Some Applications of Trigonometry

1. Why is Trigonometry a Difficult Topic for Many Students? Is there Any Method Through Which it Can be Learned Easily?

It is only a myth that trigonometry is a scarily difficult topic. Yes, it is true that some may find it difficult to solve the problems of the chapter, but every chapter may have such issues. But success lies where we do not stop trying more and more unless we become experts on the topic. As we the way to success do not have any shortcuts, the same is the trigonometry case. We have to first be thorough with all the trigonometric ratios and equations and then learn to draw diagrams in the most accurate manner and then keep on practising and practising. Our team's important questions at Vedantu can help you a lot in this process. We can assure you that none of your topics is left uncovered once you have done all the questions prepared by us. Practice questions to the maximum so that you become able to solve problems at lightning speed. Practising more is equal to scoring more and more. So, once the basics are clear, collect questions from whatever sources possible and start solving them at the earliest.

2. Is Trigonometry and Applications of Trigonometry Merely a Piece for Academic Scoring? Or Whether it Has Any Purpose in Our Daily Life?

Actually, there is a false belief that there is something merely for academics. Everything that we learn in our books will surely have some applications in our daily life. The truth is that we are just not aware of it. The same is the case for trigonometry and also for applications of trigonometry. From the name of the chapter – Applications of trigonometry itself, we can understand that it is an application-oriented chapter. In many cases, such as finding length, depth, distance, etc., were measured by the manual process can turn into a very hectic process, applications of trigonometry have helped us. Instead of using many instruments for measuring, with just a pen and paper and some trigonometric ratios, we can do the same. Trigonometry finds wide applications in the field of architecture, engineering, and many such. Besides in daily life, when coming to academics also, trigonometry is a very scoring chapter that can be easily dealt with if we have practised enough. As every bookish knowledge is meant to be applied in our life, the same is the case for trigonometry too. 

3. What is the significance of Chapter 9 “Some Applications of Geometry” of Class 10 Maths?

Chapter 9 “Some Applications of Geometry” of Class 10 Maths has much significance both from the examination perspective as well as due to its applications in our daily lives. 

For exams, this chapter is important because i) it can carry around 6 marks ii) it is a chapter that can help you score high in exams.

Moreover, this concept has several applications in fields like Engineering, Criminology, Marine Biology, Constructions, Aeronautics, Navigation, Physics, measuring the heights of buildings, mountains, etc. Hence, learning it will be beneficial. 

4. How can I download Vedantu’s Important Questions for Chapter 9 “Some Applications of Geometry” of Class 10 Maths.

To download these questions:

Click on Vedantu’s Important Questions for Chapter 9 “Some Applications of Geometry."

Click on the option to "Download PDF" when you scroll down on the following page.

This will redirect you to the next page containing the link to download the required PDF promptly.

Otherwise, you can install the Vedantu Mobile app. You can then download these important questions from the mobile app. Nonetheless, both these methods do not incur any cost. 

5. What are the significant features of Vedantu’s Important Questions for Chapter 9 “Some Applications of Geometry” of Class 10 Maths?

These are the very advantageous features of Vedantu's Important Questions:

These are cautiously selected by expert teachers.

These have been put together after screening several sample papers, mock papers, reference books, and previous years' question papers.

These have been systematically arranged as per the marking scheme of 1 to 5 marks questions.

 The solutions to these questions are prepared especially to focus on the CBSE board examinations.

These are available to be downloaded free of charge.

6. What should I do if I find Chapter 9 “Some Applications of Geometry” of Class 10 Maths difficult?

It is perfectly normal for students to find certain chapters intimidating. However, the first step to get over this is to let go of the fear. Analyze why you find the chapter complicated and work on the problem areas in parts.

Read the text thoroughly and refer to visual aids to help in enhanced understanding. Ask your teachers in case of doubts. You can also opt for Vedantu's one-on-one classes for the same. Practising a good number of problems will help you overcome any fear.

7. What are the three main topics taught in Chapter 9 “Some Applications of Geometry” of Class 10 Maths?

The three major topics that help in understanding various applications of trigonometry are as follows:

Line of sight: refers to a straight line from the eye of the observer to the object

Angle of elevation: the angle formed by the line of sight and the horizontal line. This happens in case the observer is looking upwards at the object.

Angle of depression: the angle formed by the line of sight and the horizontal line. This is used when the observer is looking downwards at the object.

CBSE Class 10 Maths Important Questions

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CBSE 10th Standard Maths Subject Some Applications of Trigonometry Case Study Questions 2021

By QB365 on 22 May, 2021

QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

QB365 - Question Bank Software

10th Standard CBSE

Final Semester - June 2015

Case Study Questions

(ii) Measure of \(\angle\) ACB is equal to

(iii) Width of the river is 

(iv) Height of the other temple is

(v) Angle of depression is always

(ii) Value of DF is equal to

(iii) Value of h is

(iv) Height of the balloon from the ground is

(v) If the balloon is moving towards the building, then both angle of elevation will

(ii) If the angle made by the rope to the ground level is 45°, then find the distance between artist and pole at ground level.

(iii) Find the height of the pole if the angle made by the rope to the ground level is 30°.

(iv) If the angle made by the rope to the ground level is 30° and 3 m rope is broken, then find the height of the pole

(v) Which mathematical concept is used here?

(ii) If fireman place the ladder 5 m away from the wall and angle of elevation is observed to be 30°, then length of the ladder is

(iii) If fireman places the ladder 2.5 m away from the wall and angle of elevation is observed to be 60°, then find the height of the window. (Take \(\sqrt{3}\) = 1.73)

(iv) If the height of the window is 8 m above the ground and angle of elevation is observed to be 45°, then horizontal distance between the foot of ladder and wall is

(v) If the fireman gets a 9 m long ladder and window is at 6 m height, then how far should the ladder be placed?

(ii) Distance between two positions of the car is

(iii) Total time taken by the car to reach the foot of the building from starting point is

(iv) The distance of the observer from the car when it makes an angle of 60° is

(v) The angle of elevation increases

*****************************************

Cbse 10th standard maths subject some applications of trigonometry case study questions 2021 answer keys.

(i) (b): The person who makes small angle of elevation is more closer to the balloon. \(\therefore\) Radlra is more closer to the balloon. (ii) (b):  \(\text { In } \Delta E F D, \tan 30^{\circ}=\frac{E D}{D F}\) \(\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{h}{D F} \) \(\Rightarrow \quad D F=h \sqrt{3} \mathrm{~m}\) (iii) (a): In \(\Delta\) GCE, \(\begin{array}{l} \tan 60^{\circ}=\frac{E C}{G C}=\frac{h+4}{D F} \\ \Rightarrow \quad \sqrt{3}=\frac{h+4}{\sqrt{3} h} \Rightarrow 3 h=h+4 \Rightarrow h=2 \end{array}\) (iv) (c): Height of the balloon from the ground = BE = BC + CD + DE = 2 + 4 + 2 = 8 m (v) (b)

(i) (c):   \(\text { In } \Delta A B C, \frac{A B}{B C}=\tan 60^{\circ}\) \(\Rightarrow \quad A B=25 \times \sqrt{3}\) \(\therefore\) Height of building is 25 \(\sqrt{3}\) m . (ii) (b):   \(\text { In } \Delta A B D, \frac{A B}{B D}=\tan 30^{\circ}\) \(\Rightarrow \frac{25 \sqrt{3}}{B D}=\frac{1}{\sqrt{3}} \Rightarrow B D=75 \mathrm{~m}\) \(\therefore\)  Distance between two positions of car = (75 - 25) m = 50m. (iii) (d): Time taken to cover 50 m distance = 6 sec. \(\therefore\) Time taken to cover 25 m distance = 3 sec. \(\therefore\) Total time taken by car = 6 sec + 3 sec = 9 sec (iv) (c):  \(\text { In } \Delta A B C, \frac{B C}{A C}=\cos 60^{\circ}\) \(\Rightarrow \quad \frac{25}{A C}=\frac{1}{2} \) \(\Rightarrow A C=50 \mathrm{~m}\) (v) (a)

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• Class 10 Maths MCQs
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Class 10 Maths Chapter 9 Some Applications of Trigonometry MCQs

Class 10 Maths Chapter 9 MCQs (Some Applications of Trigonometry) are available online here at BYJU’S with solved answers. All the objective questions are prepared as per the CBSE board syllabus (2022 – 2023) and NCERT guidelines. Practising these questions will help students to score good marks in the board exam. Also, click here to get chapter-wise multiple-choice questions.

Also, check: Heights and Distances (An application of trigonometry)

Class 10 Maths Chapter 9 MCQs (Some Applications of Trigonometry)

Solve the questions below for Chapter 9 (Some applications of trigonometry) and increase your chances of scoring high in this chapter. Also, get important questions for class 10 Maths here to practice more.

Click here to download the PDF of additional MCQs for Practice on Some Applications of Trigonometry Chapter of Class 10 Maths along with the answer key:

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Students can also get access to Some Applications of Trigonometry Class 10 Notes here.

1. If the length of the shadow of a tree is decreasing then the angle of elevation is:

(a) Increasing

(b) Decreasing

(c) Remains the same

(d) None of the above

Answer: (a) Increasing

Explanation: See the following figure:

As the shadow reaches from point D to C towards the direction of the tree, the angle of elevation increase from 30° to 60°.

2. The angle of elevation of the top of a building from a point on the ground, which is 30 m away from the foot of the building, is 30°. The height of the building is:

(b) 30/√3 m

(c) √3/10 m

Answer: (b) 30/√3 m

Explanation: Say x is the height of the building.

a is a point 30 m away from the foot of the building.

Here, height is the perpendicular and distance between point a and foot of building is the base.

The angle of elevation formed is 30°.

Hence, tan 30° = perpendicular/base = x/30

1/√3 = x/30

3. If the height of the building and distance from the building foot’s to a point is increased by 20%, then the angle of elevation on the top of the building:

(a) Increases

(b) Decreases

(c) Do not change

Answer: (c) Do not change

Explanation: We know, for an angle of elevation θ,

tan θ = Height of building/Distance from the point

If we increase both the value of the angle of elevation remains unchanged.

4. If a tower 6m high casts a shadow of 2√3 m long on the ground, then the sun’s elevation is:

Answer: (a) 60°

Explanation: As per the given question:

tan θ = 6/2√3

tan θ = tan 60°

5. The angle of elevation of the top of a building 30 m high from the foot of another building in the same plane is 60°, and also the angle of elevation of the top of the second tower from the foot of the first tower is 30°, then the distance between the two buildings is:

Answer: (a) 10√3 m

tan 60° = 30/x

6. The angle formed by the line of sight with the horizontal when the point is below the horizontal level is called:

(a) Angle of elevation

(b) Angle of depression

(c) No such angle is formed

Answer: (b) Angle of depression

The angle formed by the line of sight with the horizontal when the point is below the horizontal level is called angle of depression.

7. The angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level is called:

Answer: (a) Angle of elevation

The angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level is called angle of elevation.

8. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. The height of the tower (in m) standing straight is:

Answer: (a) 15√3

Explanation: We know:

tan (angle of elevation) = height of tower/its distance from the point

tan 60° = h/15

9. The line drawn from the eye of an observer to the point in the object viewed by the observer is said to be

(c) Line of sight

Answer: (c) Line of sight

The line drawn from the eye of an observer to the point in the object viewed by the observer is said to be line of sight.

10. The height or length of an object or the distance between two distant objects can be determined with the help of:

(a) Trigonometry angles

(b) Trigonometry ratios

(c) Trigonometry identities

Answer: (b) Trigonometry ratios

The height or length of an object or the distance between two distant objects can be determined with the help of trigonometry ratios.

11. When the shadow of a pole h metres high is √3h metres long, the angle of elevation of the Sun is

Answer: (a) 30°

Explanation:

Let AB be the pole and BC be its shadow.

Consider θ is the angle of elevation of the Sun.

In right triangle ABC,

tan θ = AB/BC = h/√3h = 1/√3

tan  θ = tan 30°

12. A ladder makes an angle of 60° with the ground, when placed along a wall. If the foot of ladder is 8 m away from the wall, the length of ladder is

Answer: (d) 16 m

Let AB be the wall, AC be the length of the ladder.

In right angled triangle ABC,

cos 60° = BC/AC

AC = 8 × 2 = 16

Therefore, the length of the ladder is 16 m.

13. If the height and length of a shadow of a tower are the same, then the angle of elevation of Sun is

Answer: (c) 45°

Let AB be the tower and BC be its shadow.

Consider the angle of elevation of the Sun as θ.

According to the given,

tan θ = AB/BC

tan θ = AB/AB {since AB = BC}

tan θ = tan 45°

14. The angle of depression of an object on the ground, from the top of a 25 m high tower is 30°. The distance of the object from the base of tower is

Answer: (a) 25√3

Let AB be the tower and BC be the distance of the object (at C) from the base of the tower.

tan 30° = AB/BC

1/√3 = 25/BC

BC = 25√3 m

15. The shadow of a tower standing on level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it was 60°. The height of the tower is 

Answer: (b) 20√3 m

When the sun’s altitude is the angle of elevation of the top of the tower from the tip of the shadow.

Let AB be h m and BC be x m. From the question, DC is 40 m longer than BC.

So, BD = (40 + x) m

And two right triangles ABC and ABD are formed as shown in the figure.

tan 60° = AB/ BC

x = h/√3….(i)

tan 30° = AB/ BD

1/ √3 = h/ (x + 40)

x + 40 = √3h

h/√3 + 40 = √3h [using (i)]

h + 40√3 = 3h

Therefore, the height of the tower is 20√3 m.

16. If the angles of elevation of the top of a tower from two points at the distance of a m and b m from the base of tower and in the same straight line with it are complementary, then the height of the tower (in m) is

(c) √(a + b)

(d) √(a – b)

Answer: (b) √ab

If the angles of elevation of the top of a tower from two points at the distance of a m and b m from the base of tower and in the same straight line with it are complementary, then the height of the tower (in m) is √ab.

17. From a point on a bridge across a river the angle of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at the height of 30 m from the banks, the width of the river is

(a) 30(1 + √3) m

(b) 30(√3 – 1) m

Answer: (a) 30(1 + √3) m

The bridge is at a height of 30 m from the banks.

Let, A and B represent the points on the bank on opposite sides of the river. And, AB is the width of the river. P is a point on the bridge which is at the height of 30 m from the banks.

AB = AD + DB

In right ΔAPD,

So, tan 30° = PD/ AD

1/√3 = PD/ AD

AD = √3(30)

AD = 30√3 m

Next, in right ΔPBD

So, tan 45° = PD/ BD

We know that, AB = AD + DB = 30√3 + 30 = 30(√3 + 1)

Hence, the width of the river = 30(1 + √3)m

18. The ratio of the height of a tower and the length of its shadow on the ground is √3 : 1. The angle of elevation of the Sun is

Answer: (c) 60°

Let AB be the height and BC be its shadow.

θ be the angle of elevation of the Sun.

According to the given, AB : BC = √3 : 1

So, AB = √3x and BC = x

tan θ = √3x/x 

19. A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance between the foot of the tree to the point where the top touches the ground is 8 m. The height of the tree is

Answer: (b) 8√3 m

Let AC be the initial height of the tree.

Due to the storm the tree is broken at B.

Let the bent portion of the tree be AB = x m and the remaining portion BC = h m.

So, the height of the tree AC = (x + h) m

And, given DC = 8m

In right ΔBCD,

tan 30° = BC/DC

Again in right ΔBCD,

cos 30° = DC/BD

x = 16/√3 m

So, x + h = 16/√3 + 8/√3

= (24 . √3)/(√3 . √3)

Therefore, the height of the tree is 8√3 m.

20. The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will be

(a) Greater than 60°

(b) Equal to 30°

(c) Less than 60°

(d) Equal to 60°

Answer: (c) Less than 60°

Let AB = h be the height and BC = x.

In this case, the angle of elevation is 30°.

When height is doubled, the height of the tower will be PQ = 2h.

In this case, consider the angle of elevation as θ.

Also, BC = QR = x.

In triangle ABC,

tan 30° = AB/BC = h/x

1/√3 = h/x….(i)

In triangle PQR,

tan θ = PQ/QR

tan θ = 2h/x

tan θ = 2(1/√3) {from (i)}

tan θ = 1.15 (approx)

θ = tan -1 (1.15) < 60°.

Video Lesson on Trigonometry

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NCERT Solutions for Class 10 Maths Ch 9 Some Applications of Trigonometry

• Exercise 9.1

How many exercises in Chapter 9 Some Applications of Trigonometry

What is line of sight, what is angle of elevation, what is angle of depression, contact form.

NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry

NCERT Solutions Class 10 Maths Chapter 9 Some Applications of Trigonometry are provided here to help the students of CBSE class 10. Our expert teachers prepared all these solutions as per the latest CBSE syllabus and guidelines. In this chapter, we have discussed the height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios. And you also learn what is the line of sight, angle of elevation, and angle of depression etc.  CBSE Class 10 Maths solutions provide a detailed and step-wise explanation of each answer to the questions given in the exercises of NCERT books.

CBSE Class 10 Maths Chapter 9 Some Applications of Trigonometry Solutions

Below we have given the answers to all the questions present in Some Applications of Trigonometry in our NCERT Solutions for Class 10 Maths chapter 9. In this lesson, students are introduced to a lot of important concepts that will be useful for those who wish to pursue mathematics as a subject in their future classes. Based on these solutions, students can prepare for their upcoming Board Exams. These solutions are helpful as the syllabus covered here follows NCERT guidelines.

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Class 10 Maths Case Study Questions Chapter 8 Introduction to Trigonometry

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Case study Questions in the Class 10 Mathematics Chapter 8  are very important to solve for your exam. Class 10 Maths Chapter 8 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 10 Maths Case Study Questions Chapter 8  Introduction to Trigonometry

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Introduction to Trigonometry Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 8 Introduction to Trigonometry

Case Study/Passage-Based Questions

Question 1:

Answer: (d) 6m

(ii) Measure of ∠A =

Answer: (c) 45°

(iii) Measure of ∠C =

(iv) Find the value of sinA + cosC.

Answer: (d) 2√2

(v) Find the value of tan 2 C + tan 2  A.

Answer: (c) 2

Question 2:

Answer: (a) 30°

(ii) The measure of  ∠C is

Answer: (c) 60°

(iii) The length of AC is 

Answer: (d)6√3m

(iv) cos2A =

Answer: (b)1/2

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Introduction to Trigonometry Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Chapter 8 Class 10 Introduction to Trignometry

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Trigonometry means studying relationship between measures of triangle. Usually, we talk about right triangles when we study trigonometry,

In this chapter, we will study

• What is sin, cos, tan ( Sine, cosine, tangent) ... and how they are found in a triangle
• What is sec, cosec, cot, and how is it related to sin, cos, tan.
• (Sin, cos, tan, sec, cosec, cot are known as Trigonometric Ratios)
• Then, we study Trigonometric ratios of specific angles l ike 0°, 30°, 45°, 60°, 90° ; and do some questions
• We study the formulas of sin (90 - θ) , cos (90 - θ), tan (90 - θ)
• And then we study Trigonometric Identities, and how other identities are derived from sin 2 θ + cos 2 θ = 1

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