Question

A tower subtends an angle α at a point A in the plane of its base and the angles of depression of the foot of the tower at a point b metres just above A is β. Prove that the height of the tower is b tan α cot β.

Answer 1

Let be the height of tower. The tower CD subtends an angle at a point. And the angle of depression of foot of tower at a point b meter just above is. Let and, .

Here we have to prove height of tower is

We have the corresponding figure as follows

So we use trigonometric ratios.

In,

Again in

Hence the height of tower is .