Question

The angle of elevation of a cloud from point 200 meter above a lake is 30° and the angle of depression
of its reflection in the lake is 60°. Find the height of the cloud.
​

Answer 1

AB is the surface of lake. C’ is the reflection of cloud ‘C’.

∠CPM = 30° and ∠C'PM = 60°

Let, C M = h metre

CB = (h + 200) metre

C'B = (h + 200) metre

In ∆CMP,

tan 30° =  

CM

PM

⇒  

1

=  

h

√3 PM

⇒ PM = √3 h ....(i)

In ∆PMC',

tan 60° =  

C'M

PM

⇒ tan 60° =  

C'B + BM

PM

⇒ √3 =  

h + 200 + 200

PM

⇒ PM =  

h + 400

.... (ii)

√3

From equations (i) and (ii) ,

√3 h =  

h + 400

√3

⇒ 3h = h + 400

⇒ 2h = 400 ⇒ h = 200

∴ CB = h + 200 = 400 metre

Note : If the angle of elevation of a cloud from a point h metre above a lake is a and the angle of depression of its reflection in the lake is b, then

The height of the cloud =  

h( tanβ + tanα )