**If the angle of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its … cloud is h(tan β +…**

###### Answers:

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.

tan Alpha=H-h/x

X=H-h/tan alfa

tan beta =H+h/x

Tan beta =H+h/H-h/tan alfa

Tan beta=tan alfa (H+h)/H-h

Tan beta (H-h)=Htan alfa + htan alfa

Htan beta -Htan alfa=htan alfa + htan beta

H(tan beta -tan alfa ) = h(tan alfa+tan beta )

H=h(tan alfa+tan beta)/tan beta-tan alfa