The angle of elevation of the top of a tower from two points on the gr – InterviewSolution

InterviewSolution

1.	The angle of elevation of the top of a tower from two points on the ground at distances a metres and b metres from the base of the tower and in the same straight line are complementary.Prove that height of the tower is` sqrt(ab)`.
Answer» Let height of tower is h. Let angle at distance a is `alpha`. Then, from distance b, it will be `90-alpha`. Then, `tanalpha = h/a` (eq 1) `tan(90-alpha) = h/b ``cotalpha = h/b` `tanalpha = b/h` (eq 2) From equations1 and 2, `h/a = b/h` `h^2 = ab` `h=sqrt(ab)`

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