Question

the angle of elevation of a cloud from a point 60m above the surface of the water of a lake is 30 and the angle of depression of its shadow fron the same point in water of the lake is 60 find the height of the cloud from the surface

Answer 1

Answer:

120 m

Step-by-step explanation:

From figure :

Let AO = h m.

Given,

The angle of elevation of a cloud from a point 60 m above.

Thus, CD = OB = 60 meters .

Then,

EB = AB = AO + OB = 60 + h

From the figure,

In Δ  AOD,

=> tan 30 = AO/OD

=> 1/√3 = h/OD

=> OD = h√3

In Δ EOD,

=> tan 60 = OE/OD

=> √3 = (OB + BE)/OD

=> √3 * OD = OB + BE

=> √3 * h*√3 = 60 + 60 + h  

=> 3h = 120 + h

=> 3h - h = 120

=> 2h = 120

=> h = 120/2

=> h = 60

Then,

height = AB + BE = 60 + 60 = 120 m.

Therefore, height of the cloud from the surface = 120 m.

Hope it helps!