Q. 54.8( 5 Votes )

If the angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complimentary, find the height of the tower.

Answer :


Let the height of the tower be h meters


Given, the angles of elevation of the top of a tower from two points are complimentary


ACB = θ and ADB = 90° - θ


In Δ ABC


tan θ = 4 / h


h = 4tan θ…………1


In ΔABD


tan (90° - θ) =


h = 9 (cot θ) ………………..( tan (90° - θ) = cot θ ) 2


cot θ = h/9


cot θ =


1/tan θ =


9 = 4 tan2θ


tan θ = 3/2


Height of tower (h)= 4 × 3/2………..putting value of tan θ in 1


= 6m


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