Question

The horizontal distance between two towers is 75 m and the angular depression of the top of the first tower as seen from the top of the second, which is 160 m high, is 45°. Find the height of the first tower.

Answer 1

Let AB and CD be the two towers. 

The height of the first tower is AB = 160 m 

The horizontal distance between the two towers is BD = 75 m 

And the angle of depression of the first tower as seen from the top of the second tower is ∠ACE = 45°

In ΔACE,

`(AE)/(EC) = tan 45^circ = 1`

`=>` AE = EC = BD = 75 m

∴ CD = EB

= AB – AE

= (160 – 75)

= 85 m

Hence, height of the other tower is 85 m.