Question

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

Answer 1

Let AO = H

CD = OB = 60 m

A' B = AB = 60 + H

 

In ∆ AOD,



Now, In ∆ A'OD,



⇒ 120 + H = 3H

⇒ 2H = 120

⇒ H = 60 m

 

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

Answer 2

Answer:

Let A be the cloud and D be its shadow.

BC = 60 m  

Height of cloud = h m .

Total height of cloud = h + 60 m  

In  Δ ABE

h / x = tan 30

x = h √ 3

In Δ BDE

h + 60 + 60 / x  = tan 60

h + 120 = x √ 3

2 h = 120

h = 60 m .

Therefore , height of cloud from surface of water = ( 60 + 60 ) = 120 m .