The angles of elevation of the top of a tower from two points P and Q at a distance of a and b respectively from the base and in same straight line with it are complimentary. Prove that the height of tower is √ab
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AB is a tower. D and Care two points on the same side of a tower, BD = a and BC = b.
∠ADB and ∠ACB are the complementary angles.
If ∠ADB = x, then ∠ACB = 90 – x
In ∆ADB
…… (1)
In ∆ABC,
…....(2)
Multiplying (1) and (2),
(AB)2 = ab
AB = √ab
Height of tower = AB = √ab
Hence proved.
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