Angle Elevation Cloud Point Metres Above Angle Depression Reflection Prove Height Cloud

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 +…


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