Question

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

Answer 1

Answer: 120m

Step-by-step explanation: let the h be h+60 and reflection height be 60+60+h= 120+h

Tan 30°= h/x

x= distance between the point and the cloud

1/√3=h/x

x=h√3

Tan60°= h+120/x

√3=h+120/h√3

h+120=3h

h=60m

Height oft cloud from lake =h+60

=120m

Hope it helps

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 .