Question

The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 30 0 and the angle of depression of its shadow from the same point in water of lake is 60 0 . Find the height of the cloud from the surface of water

Answer 1

Let AO=H
CD=OB=60m
A'B=AB=(60+H)m

In triangke AOD,
tan30°=AO/OD=H/OD

H=OD/√3
OD=√3 H

Now, in triangle A'OD,

tan60°=OA'/OD=(OB+BA')/OD
√3=(60+60+H)/√3 H
    =(120+H)/√3 H
 =>120+H=3H
      2H=120
       H=60m

Thus,
Height of the cloud above the lake = AB+A'B
                                                                 =(60+60)
                                                                 = 120m
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