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Question

If the angle of elevation of a cloud from a point 200 mabove a lake is 30and 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:


  1. 400 m

  2. 30 m

  3. 200 m

  4. 500 m


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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