A tower subtends an angle α at a point A in the plane of its base and the angle 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.

Question

A tower subtends an angle &#x3B1; at a point A in the plane of its base and the angle of depression of the foot of the tower at a point b metres just above A is &#x3B2;. Prove that the height of the tower is b tan &#x3B1; cot &#x3B2;.

Philoid · Accepted Answer

In the fig let CD is the height of tower

CD = a + b

In ∆ABD

Cot β =

x = b Cot β ………………(1)

In ∆ADC

tan α =

⇒ CD = b Cot β tan α

Therefore height of the tower is b Cot β tan α