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From a point a metres above a lake the a...

From a point a metres above a lake the angle of elevation of a cloud is `alpha` and the angle of depression of its reflection is `beta`. Prove tha the height of the cloud is
`(a sin(alpha + beta))/(sin(beta-alpha))` metres.

Text Solution

Verified by Experts

[ Hint : In `DeltaPMC, tan alpha = (h-a)/(PM)`
`rArr PM = (h-a) cot alpha`………………………(1)
In `DeltaPMC', tan beta = (h+a)/(PM)`
`rArr " "h =(h-a) cot alpha tna beta - a`
`rarr h= (a(sin alpha cos beta + cos alpha sin beta ))/(sin beta cos alpha - sin alpha cos beta )`
`rArr h=(a sin(alpha + beta))/(sin(beta-alpha))` metres (Proved)]
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