Angle of Elevation: Overview, Questions, Preparation

The angle of elevation is formed when an observer views a point above the horizontal plane. In other words, it is the angle formed at the point considered by the line of sight along with the horizontal plane, i.e. horizontal line of sight. It is the angle formed when we raise our heads to look at a particular object above the ordinary line of sight.

Line of Sight - it is the level drawn from the observer's eyes till the viewed point.

Horizontal - it is a straight line over the flat surface of the coordinate. It is the line at which all the points have the same y-coordinate.

Angle - two line segments that meet at a common endpoint is called an angle.

The formula for elevation angle depends on the information provided such as measurements of the sides of the angle and distance from the object.

If the distance and height are given, use the following formula to find the angle of elevation -

tangent of the angle of elevation = the given height of object/distance given from the object

Students can expect questions from this topic for about six marks in the examination.

1. The angle of elevation of a tower's top as viewed from a certain point on the ground is 30°. The point at which the top is viewed is 30m away from the foot of the tower. Ascertain the height of the tower.

Let the tower’s height be x.

tan 30° = AB/BC

or 1/√3 = x/30

or x = 10√3

Therefore, the height of the tower is 10√3m.

 2. Find out the height of a tree from which a person is standing 20 feet away. The angle of elevation is 38°.

Let's assume the height of the individual is 5 feet.

Add 5 feet to the height of the tree to calculate the total height.

Let the height of the tree be x,

tan 38° = x/20

x = 20tan 38°

x = 15.63 (approx.)

Therefore, the height of the tree is 20.63 feet (approx.)

3. The angle between the horizontal and a kite in the sky is 40°. The shadow of the kite falls directly beneath the kite. The shadow is 200 feet away from an individual standing on the ground. The height of the individual is 6 feet. How high is the kite in the sky?

Tangent function can be used to find out the height of the kite in the sky.

tan 40° = height / 200

height = 200 tan 40°

height = 200 x 0.839

height = 167.8

Therefore, the height of the kite is 167.8 feet.

Q: How can the angle of elevation be explained with an example?

Q: How do you find height when the angle of elevation is provided?

Q: What is the angle of depression?

Q: How does the angle of depression differ from the angle of elevation?

Q: What is the line of sight?