If the angle of elevation of a cloud from a point *h* metres above a lake is *alpha* and the angle of depression of its reflection is *beta*. Prove that the height of cloud is *h(tan beta + tan alpha)/ tan beta - tan alpha*

Let AN be the surface of the lake and O be the point of observation such that OA =* h* metres.

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

Then PN = P'N

Let OM ⊥ PN

Also, ∠POM = α and ∠P'OM = β

Let PM = *x*

Then PN = PM + MN = PM + OA = *x + h*

In rt. ΔOPM, we have

In rt. ΔOMP', we have,

**Equating (1) and (2):**

Hence, height of the cloud is given by PN = *x + h*

Hence proved.

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