Question

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

Answer 1

hey mate
here's the solution

Answer 2

$\huge\bold\red{ANSWER--}$


Let AO = H

CD = OB = 60 m

A' B = AB = 60 + H

 

In ∆ AOD,

tan30°=AO/OD=H/OD

H=OD/√3

OD=√3H

Now, In ∆ A'OD,

tan60°=OA'/OD=OB+BA'/OD

√3=60+60+H/√3H=120+H/√3H

⇒ 120 + H = 3H

⇒ 2H = 120

⇒ H = 60 m


Thus, height of the cloud above the lake = AB + A'B = 60 + 60 = 120 m.