NCERT Solutions for class 10 Maths Chapter 9 Some applications of Trigonometry Exercise 9.1 in English Medium and Prashnavali 9.1 in Hindi Medium, free to download for session 2022-2023.

• ## 10th Maths Chapter 9 Exercise 9.1

### Class 10 Maths Chapter 9 Solutions

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 Class: 10 Maths (English and Hindi Medium) Chapter 9: Some applications of Trigonometry

#### 10th Maths Chapter 9 Solutions

NCERT Solutions for class 10 Maths Chapter 9 in English & Hindi Medium free to use online or download in PDF format for offline or View in Video Format also. Join the discussion forum to ask your doubts and discuss your education queries.

#### Class 10 Maths Chapter 9 Exercise 9.1 Solutions in Videos

Class 10 Maths Exercise 9.1 Question 1 to 9 Solutions
Class 10 Maths Exercise 9.1 Question 10 to 16 Solution

### What is the use of Trigonometry in daily life?

Trigonometry has wide application in solving problems related to real life situations. One of the best methods for the indirect measurement of length or height involve trigonometric rations. Trigonometry is extensively used in geography, navigation, astronomy, etc. The knowledge of trigonometry is used to construct maps, determine the position of different islands in relation to the longitudes and latitudes.

### What is horizontal ray?

Horizontal Ray: A ray parallel to the surface of the Earth emerging from the eye of an observer is called a horizontal ray.

### What do you understand by Line of Sight?

Line of Sight: The line of sight (or ray of vision) is the line drawn from the eye of an observer to the point in the object viewed by the observer.

### What do you mean by Angle of Elevation?

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

### What is Angle of Depression?

Angle of Depression: The angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level.

### What is line of sight?

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

### How do you find an angle of elevation?

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

### What is meant by angle of depression?

The angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level.

### How can we find the height of an object without measuring?

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

#### Previous Years Questions

ONE MARK QUESTIONS
1. The ratio of the height of a tower and the length of its shadow on the ground is √3:1. What is the angle of elevation of the sun? [CBSE 2017]
THREE MARKS QUESTIONS
1. From the top of a 7 m high building, the angle of elevation of the top of a tower is 60 and the angel of depression of its foot is 45. Find the height of the tower. [CBSE 2017]
FOUR MARKS QUESTIONS
1. Two points A and B are on the same side of a tower and in the same straight line with its base. The angles of depression of these points from the top of the tower are 60 and 45 respectively. If the height of the tower is 15 m, then find the distance between these points. [CBSE 2017]

##### Historical Facts!

1. Surveyors have used trigonometry for centuries. One such large surveying project (which is used for measuring angles with a rotating telescope) of the nineteenth century was the ‘Great Trigonometric Survey’ of British India for which the two largest-ever theodolites were built.
2. During the survey in 1852, the highest mountain in the world was discovered. From a distance of over 160 km, the peak was observed from six different stations.
3. In 1856, this peak was named after Sir George Everest, who had commissioned and first used the giant theodolites. The theodolites are now on display in the Museum of the Survey of India in Dehradun.

###### Golden Words

The mathematician does not study mathematics because it is useful. He study it because he delights in it and he delights in it because it is beautiful. … Henri Poincare

### What should we recall before starting chapter 9 of class 10 Maths?

Before starting chapter 9 Some Applications of Trigonometry of class 10 math students should revise all formulas and identities mentioned in chapter 8 Introduction to Trigonometry of class 10 math. If students remember all formulas and identities mentioned in chapter 8 on tips then chapter 9 becomes easy to understand.

### What are the main topic to study in Class 10 Maths NCERT Chapter 9?

In chapter 9 Some Applications of Trigonometry of class 10 math, students will study how trigonometry is used for finding the heights and distances of various objects, without actually measuring them. Also in this chapter students will see the meaning of Angle of Elevation and Angle of Depression.

### How many exercise are there in chapter 9 of 10th Math?

There is only 1 exercise (Exercise 9.1) having 16 questions and 7 examples in chapter 9 of class 10 math. All the examples and questions of this exercise are good. This chapter needs lot of practice.

### What are real life applications of trigonometry in 10th Maths Chapter 9?

Trigonometry is one of the most ancient subjects studied by scholars all over the world. It was invented because its need arose in astronomy. Some real life applications of trigonometry are:

1) To calculate distances from the Earth to the planets and stars.
2) Trigonometry is used in geography and in navigation.
3) The knowledge of trigonometry is used to construct maps, to determine the position of an island in relation to the longitudes and latitudes.
4) To calculate height of buildings, towers and monuments.       