The angle of elevation of the top of tower from 2 points p and q at a distance a and b respectively from the base and in the same straight line with it are complementary . Prove that the height of the tower is √ab .
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hope it helps you for such questions simply make one side of two equations equal .As complementary angles sum 90
let first angle be theta and second 90-theta
let first angle be theta and second 90-theta
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Let h be the height of the tower, A and B be the angles of elevation from two points at distance a and b, respectively. B = 90 - A.
Then h = a tanA and h = b tanB = b tan(90 - A) = b cotA = b/tan A
so h^2 = a tanA * b/tan A = ab
h = sqrt(ab)
Then h = a tanA and h = b tanB = b tan(90 - A) = b cotA = b/tan A
so h^2 = a tanA * b/tan A = ab
h = sqrt(ab)
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