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From te top of a tower , 60 meters high,...

From te top of a tower , 60 meters high, the angles of depression of the top and bottom of a pole are `alpha and beta ` respectively .Find the height of the pole.

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Let AE be the tower ,CD be the pole and d be the distance between the tower and the pole .Also let h be the height of the pole.

In triangle ABC d=(60 h ) cot `alpha`
In triangle AED , d = 60 cot `beta`
`therefore 60 cot beta =(60 -h ) cot alpha`
`rArr h=(60 (cot alpha - cot beta )/(cot alpha))`
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