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The angle of elevation of the top of a ...

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)`.

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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,
...
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