Question

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Question
If the angle of elevation of a cloud from a point h metres above the surface of a lake is 'a' and the angle of depression of its reflection in the lake is 'ß', prove that the height of the cloud is
$\frac{h(tan \beta + tan \: \alpha) }{tan \beta - tan \: \alpha } metres.$

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Answer 1

Answer:

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Answer 2

Answer:

Let AB be the surface of the lake and let P be a point of observation such that AP = h metres.

Let C be the position of the cloud and C' be its reflection in the lake.

Then, CB=C'B. Let PM be perpendicular from P on CB. Then, ∠CPM= α and ∠MPC' = β. Let CM = x.

Then, CB=CM+MB=CM+PA = x+h

In △ CPM, we have,

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