Q. 535.0( 4 Votes )

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.

Answer :

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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