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Question

If the angle of elevation of a cloud from a point 200 m above a lake is 30 and the angle of depression of the reflection of the cloud in the lake from the same point is 60, then the height of the cloud above the lake is:


A

400 m

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B

500 m

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C

30 m

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D

200 m

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Solution

The correct option is A

400 m



In ABC',
tan60=x+400AB
3=x+400AB
AB=x+4003___(i)

In ABC,
tan30=xAB
13=xAB
AB=x3 _______(ii)

Plugging the value of AB from equation (ii) in equation (i), we get
x3=x+4003
3x=x+400
x=200 m
Hence, the height of the cloud above the lake is
200 + 200 = 400 m


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