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Question

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

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Solution

In the above figure, C is the cloud and F is its reflection on the surface of the lake AB. And E is the point of observation.

In CDE,
tan30=CDDE13=xyy=3x(i)

According to laws of reflection, BC will be equal to BF.
So,
BF=BC
=BD+DC
=60+x

In EDF,
FD=BF+BD
=60+x+AE
=60+x+60
=120+x

So,
tan60=FDDE3=120+xy3×3x=120+x[By using (i)]3xx=1202x=120x=60 m

So, the height of the cloud from the surface of the lake will be,
BC=60+x
=60+60
=120 m

1171080_1275013_ans_56024ab82aeb44cd84ad9eafe1b8b8f1.png

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