PQ is a post of given height a, and AB is a tower at some distance. If α and β are the angles of elevation of B, the top of the tower, at P and Q respectively. Find the height of the tower and its distance from the post.

In the fig PQ is the post off height ‘a’ and AB is the tower of height ‘h’


In ∆BAP


tan α =


tan α =


AP = h tan α …………………………(1)


In ∆BRQ


tan β =


tan β =


AP = ………………………(2)


From eqn (1) and (2) we get,



=


h tan β = (h-a) tan α


h tan β = h tan α – a tan α


h (tan α - tan β) = a tan α


h =


Therefore height of the tower is


Now AP = =


⇒


⇒


Therefore distance is ⇒


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