Question

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

Answer 1

The answer to this question is as follows -

Let AO = h meters

CD = OB = 60 meters

EB = AB = AO + OB = 60 + h

From the figure,

In triangle AOD,

     tan 30 = AO/OD

=> 1/√3 = h/OD

=> OD = h*√3

Now, in triangle 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

Now, the height of the cloud above the lake = AB + BE = 60 + 60 = 120 meters

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