Question

A 20 m high vertical pole and a vertical tower are on the same level ground in such a way that the angle of elevation of the top of the tower, as seen from the foot of the pole is 60° and the angle of elevation of the top of the pole, as seen from the foot of the tower is 30°. Find:

1. the height of the tower;
2. the horizontal distance between the pole and the tower.

Answer 1

Let AB be the tower and CD be the pole.

Given, CD = 20 m, ∠ADB = 60° and ∠CBD = 30°

In ΔBDC, 

`(CD)/(BD) = tan 30^circ`

`=> BD = 20sqrt(3)  m`

In ΔDBA, 

`(AB)/(BD) = tan 60^circ = sqrt(3)`

`=> AB = 20sqrt(3) xx sqrt(3) = 60  m`

Hence, 

i. Height of the tower = 60 m 

ii. Horizontal distance between the pole and tower 

= 20 × 1.732

= 34.64 m