Question

The angle of depression from the top of a tower of a point A on the ground is ${30}^{\circ }$ . On moving a distance of 20 metres from the point A towards the foot of the tower to a point B, the angle of elevation of the top of the tower from the point B is ${60}^{\circ }$. Find the height of the tower and its distance from the point A.

Answer 1

Let CD be the tower.

Suppose BC = x m and CD = h m.

Given, ∠ADE = 30° and ∠CBD = 60°.

∠DAC = ∠ADE = 30° (Alternate angles)

In ΔACD,

In ΔBCD,

From (1) and (2), we have

∴ 20 + x = 3x

⇒ 2x = 20

⇒ x = 10

∴ Height of the tower =

Distance of tower from A = AC = (20 + x) m = (20 + 10) m = 30 m