# NCERT CBSE Class 10th Mathematics Chapter 9: Some Applications of Trigonometry

Safalta Expert Published by: Sylvester Updated Wed, 22 Jun 2022 06:48 PM IST

## Highlights

NCERT CBSE Class 10th Mathematics Chapter 9: Some Applications of Trigonometry

The ninth chapter in Mathematics textbook is 'Some Applications of Trigonometry'.

### Line of Sight

When an observer looks from a point E (eye) at an object O then the straight line EO between the eye E and the object O is called the line of sight.

### Horizontal

When an observer looks from a point E (eye) to another point Q which is horizontal to E, then the straight line, EQ between E and Q is called the horizontal line.

### Angle of Elevation

When the eye is below the object, then the observer has to look up from the point E to the object O. The measure of this rotation (angle θ) from the horizontal line is called the angle of elevation.

### Angle of Depression

When the eye is above the object, then the observer has to look down from the point E to the object. The horizontal line is now parallel to the ground. The measure of this rotation (angle θ) from the horizontal line is called the angle of depression.

### The topics discussed in this chapter are as follows:

• Horizontal Level and Line of Sight
• Angle of elevation
• Angle of depression
• Calculating Heights and Distances

## 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

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

x = 30/√3

## 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

We know:

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

tan 60° = h/15

√3 = h/15

h = 15√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 ___________.

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.

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

Angle of depression

## 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