Question

From the top of a 30m high building the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. Find the height of the tower.

Answer 1

 

The diagram is in attachment section .

Let the height of the tower be x .

Let the distance between the tower and building be d .

tan 30 =  ( x - 30 ) / d

= > 1/√3 = ( x - 30 ) / d

= > d = √3( x - 30 )

Also :

tan 60 = x / d

= > √3 = x / d

= > d = x / √3

This means :

x / √3 = √3 ( x - 30 )

= > x = 3 ( x - 30 )

= > x = 3 x - 90

= > 2 x = 90

= > x = 90/2 = 45

The height is 45 m.