Q23 of 25 Page 9

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.

To find: height of the tower.


Formula Used:



Explanation:



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) = cot θ)


h = 9 (cot θ) ….. (2)





9 = 4 tan2θ


tan θ = 3/2


putting value of tan θ in 1


Height of tower


= 6m


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