Question

${\LARGE{\underline\underline{\bf{Question : }}}}}$

If the angle of elevation of a cloud from a point 'h' metres above a lake is x and the angle of depression of its reflection in the lake is y, then the distance of tue cloud from the point of observation is?? ..​

Answer 1

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