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

Our NCERT Solutions for Class 10 Maths Chapter 9 – Some Applications of Trigonometry are drafted on the latest guidelines given by CBSE. Our solutions of exercises given in CBSE NCERT Solutions Class 10 Maths Chapter 9 are concise, accurate and easy to understand. Some of the topics covered in this chapter include heights and distances, line of sight, angle of elevation, and angle of depression.

Some Applications of Trigonometry lets you appreciate the usage of the topics given in this chapter in a comprehensive manner and also clears all your doubts related to this topic. It is highly beneficial for revising and effectively retaining the fundamentals of trigonometry given in NCERT Class 10 Maths Chapter 9. These solutions help you to strengthen your foundation and move ahead with concrete knowledge to higher grades.

Maths Chapter 9 – Some Applications of Trigonometry are easy to understand and conceptually clear, helping you to score good marks in your board examinations as well as excel in competitive exams. Preparation for examination becomes an easy task when you follow the content given in our smart NCERT Solutions thoroughly.

## NCERT Class 10 Maths Chapter 9: Important Topics

This chapter deals with the application of trigonometry. Class 10 Maths, Some Applications of Trigonometry, provides you with efficient methods of studying and solving problems that shall be asked from this chapter in your board exams. In NCERT Class 10 Maths Chapter 9, you will learn the use of trigonometry in finding the heights and distances of various objects, without measuring them. Some of the important concepts covered here have been discussed below.

**Introduction**

This part of NCERT CBSE Class 10 Maths Chapter 9 tells you that trigonometry is one of the old subjects studied all over the world. Knowledge of trigonometry is used in astronomy, geography, navigation, constructing maps etc.

**Heights and Distances**

This portion of chapter 9 given in CBSE NCERT Solutions for Class 10 Maths Book tells you about the applications of trigonometry and terms related to it in real-life situations. It teaches you how to determine the height of a building or historical monument when the angle of elevation and distance is given, without actually measuring it. Similarly, you will also learn how to find the angle of elevation, angle of depression, the distance of the object using the other information given in the problem.

In order to use NCERT Solutions for Class 10 Maths Chapter 9 – Some Applications of Trigonometry, you need to understand the following terms given in chapter –

**Line of sight- is the line made from the eye of the viewer to the point in the object being viewed.**

**The angle of the elevation-**The angle of elevation of the point observed, is the angle created by the line of sight with the plane when the point being seen is above the horizontal level, i.e., the case when we elevate our head to look at the object.**The angle of depression-**The angle of depression of a point on the entity being observed is the angle made by the line of vision with the horizontal when the point is lower than the horizontal level, i.e., the situation when we lower our head to see the point being viewed.

### NCERT CBSE Class 10 Maths Chapter 9 Exercise

NCERT Solutions for Class 10 Maths Chapter 9 – Some Applications of Trigonometry are the best-described solutions for all 16 questions given in the exercise of this chapter. This exercise covers all topics from the chapter.

NCERT CBSE Class 10 Maths Chapter 9 tells you that the following points should be kept in mind while solving the trigonometric questions-

(i) You need to make an imaginary right angle using the height of the object and line of sight. Distance is usually the base of the triangle or length of horizontal level in some cases when it forms the base of the imaginary triangle.

(ii) The hypotenuse of the triangle in problem is actually the line of sight. Sometimes, we can also calculate the length of hypotenuse by using the values given for the distance of the object (base of the triangle) and length of the object (height).

(iii) The angle of elevation or depression can be calculated using the trigonometric ratios and identities.

(iv) Sometimes we need to create/imagine two right-angled triangles having a common height or two merged triangles such as one right-angled triangle inside another right-angled triangle; in order to calculate the distance between two objects from a single point.

The NCERT Solutions for Class 10 Maths Chapter 9 – Some Applications of Trigonometry are prepared in a stepwise manner to impart utmost clarity to the learner. The components of the exercise are as follows –

- Questions 1 and 2 give information about the hypotenuse of the imaginary right-angled triangle. With the given information along with the angle of elevation. You are asked to calculate the length/height of the object.
- In questions 3 and 5 of CBSE NCERT Class 10 Maths Chapter 9, the height of an object, and angle of elevation are given, and the hypotenuse of the imaginary right-angled triangle is to be determined.
- In question 4 the horizontal distance between the base of the tower and point on the ground, which gives the base of the triangle along with the angle of elevation is given. You are supposed to find the value of height.
- Questions 6 and 14 ask you to imagine two right-angled triangles in which angles of elevations are different, height is the same and you need to determine the relationship between the lengths of their bases.
- Questions 7 and 8 ask you to imagine two right-angled triangles in which angles of elevations are different, lengths of their bases are the same, and you need to determine the relationship between the heights.
- Question 9 asks you to imagine two right-angled triangles having a common base, but two different heights, one of which is given and the other is to be determined.
- Question no. 10 asks you to imagine two right-angled triangles starting from a single point and faced towards opposite directions, the sum of the length of their bases is given, base and heights are to be determined.
- Questions 11 and 16 ask you to imagine two right-angled triangles in which angles of elevations are different, height is the same which is to be determined and the relation between the lengths of their bases is given.
- In question 12 of Class 10 Maths, Some Applications of Trigonometry, angle of elevation and angle of depression is given, you need to determine the height.
- In questions 13 and 15 height and angle of depressions are given, you need to determine the relationship between the bases.

NCERT Solutions for Class 10 Maths Chapter 9 – Some Applications of Trigonometry are prepared using the best methods to solve this type of questions and help you understand complex concepts easily.