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’


tan α =

tan α =

AP = h tan α …………………………(1)


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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