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The angle of elevation of the top of a tower from two points distant a and b (a > b) from its foot and in the same straight line from it are 30° and 60°. The height of the tower is
1) a + b
2) √ab
3) √(a+b)
4) ab
The angle of elevation of the top of a tower from two points distant a and b (a > b) from its foot and in the same straight line from it are 30° and 60°. The height of the tower is
1) a + b
2) √ab
3) √(a+b)
4) ab
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)`