# 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.

In the fig let CD is the height of tower

CD = a + b

In ∆ABD

Cot β =

Cot β =

x = b Cot β ………………(1)

tan α =

tan α =

CD = b Cot β tan α

Therefore height of the tower is b Cot β tan α

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