Trigonometry application

Question

The angle of elevation of a cloud from a point h metres above a lake is theta the angle of depression of its reflection is 45 the height of cloud is 
(A)htan(45+ theta) 
(B)hcot (45 minus theta)
(C)htan(45 minus theta)
(D)hcot(45+theta)

Please answer fast

Answer 1

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.