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

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Last updated date: 09th Apr 2024
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MVSAT 2024

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.


Download CBSE Class 10 Maths Important Questions 2024-25 PDF

Also, check CBSE Class 10 Maths Important Questions for other chapters:

CBSE Class 10 Maths Important Questions

Sl.No

Chapter No

Chapter Name

1

Chapter 1

Real Numbers

2

Chapter 2

Polynomials

3

Chapter 3

Pair of Linear Equations in Two Variables

4

Chapter 4

Quadratic Equations

5

Chapter 5

Arithmetic Progressions

6

Chapter 6

Triangles

7

Chapter 7

Coordinate Geometry

8

Chapter 8

Introduction to Trigonometry

9

Chapter 9

Some Applications of Trigonometry

10

Chapter 10

Circles

11

Chapter 11

Constructions

12

Chapter 12

Areas Related to Circles

13

Chapter 13

Surface Areas and Volumes

14

Chapter 14

Statistics

15

Chapter 15

Probability

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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.


Angles

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.

 

Question 1

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.

 

Question 2

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

 

Question 3

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

 

Question 4

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

 

Question 5

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.



Vedantu- The Best Source for Exam Preparation

  1. Expert-Curated Questions:

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  1. In-Depth Knowledge Gain:

  • Practising Vedantu's important questions offers profound insights into the topic.

  • Clarifies fundamental concepts, fostering a clear understanding.


  1. Board Exam Success Strategy:

  • Solving these important questions is essential for students aiming to excel in board exams.


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  • Ensures the maths paper becomes manageable, contributing to success in exams.


  1. Parental Guidance Recommendation:

  • Parents are encouraged to recommend Vedantu's important questions for Class 10 Maths Chapter 9.

  • Simplifies applications of trigonometry, making it easier for students.


  1. Vedantu's Support Commitment:

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  • Assures that the chapter offers the best and most essential questions, ensuring interest and ease of understanding.


Conclusion

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.