From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.

Solution:

Let BC be the 20 meter high building.

The elevation is taken from D, which is a point on the ground.

Transmission tower’s height = AC – BC = AB

We need to find: The height of the tower i.e. AB,

From figure, In right angle ΔBCD,

BC/CD = tan 45°

1 = 20/CD

CD = 20

Again,

In right ΔACD,

AC/CD = tan 60°

AC/20= √3

AC = 20√3

Now, AC – BC = AB = (20√3-20) = 20(√3-1)

As a result, transmission tower’s height is  20(√3 – 1) m.