Q. 554.5( 4 Votes )

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.

Answer :

In the fig let CD is the height of tower



CD = a + b


In ∆ABD


Cot β =


Cot β =


x = b Cot β ………………(1)


In ∆ADC


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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