The top of a 12 m high tower makes an angle of depression of 60° with the bottom of an electric pole and angle of depression of 30° with the top of the pole. What is the height of the electric pole?

Correct option is C

Given:

The height of the tower = 12 m

The angle of depression from the top of the tower to the bottom of the electric pole = 60°

The angle of depression from the top of the tower to the top of the electric pole = 30°
We need to find the height of the electric pole.

Solution:

Let, h be the height of the electric pole,

d be the horizontal distance from the bottom of the tower to the bottom of the electric pole.

From the given problem:

The total height from the top of the tower to the top of the pole = 12 - h meters.

The horizontal distance d from the tower to the pole is the same for both angles of depression.

From the top of the tower to the bottom of the electric pole:

​$$\tan(60^\circ) = \frac{12}{d}$$​

​$$\sqrt{3} = \frac{12}{d}$$​

​$$d = \frac{12}{\sqrt{3}} = 4\sqrt{3}$$​

From the top of the tower to the top of the electric pole:

​$$\tan(30^\circ) = \frac{12 - h}{d}$$​

​$$\frac{1}{\sqrt{3}} = \frac{12 - h}{d}$$​

​$$\frac{1}{\sqrt{3}} = \frac{12 - h}{4\sqrt{3}}$$​

4 = 12 - h

h = 12 – 4 = 8 m
The height of the electric pole is 8 m.