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A tower subtends an angle alpha at a poi...

A tower subtends an angle `alpha` at a point A in the plane of its base and angle of depression of the foot of the tower at a point l metres just above A is `beta`. Prove that the height of the tower is l tan`alpha cot beta`.

Text Solution

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[Hint : `tan alpha = (h)/(OA)`
`rArr OA = h cot alpha`…………..(1)
`tan beta = (1)/(OA)`
` =(l)/(h cot alpha)` [by (1) ]
`rArr h cot alpha tan beta = l`
`rArr = (l)/(cot alpha tan beta ) rArr" " h=l tan alpha cot beta` (Proved) ]
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