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AP EAMCET2011MathematicsHeights and Distances

The angle of elevation of a stationary cloud from a point 2500 ~m above a lake is 15^ and from the same point the angle of depression of its reflection in the lake is 45^ . The height (in metres) of the cloud above the lake, given that 15^ =2+ 3 , is

Options

  1. A2500
  2. B2500 2
  3. C2500 3
  4. D5000

Correct answer

C. 2500 3

Step-by-step solution

In E C D 15^ = E C C D array ll & E C=C D 15^ & E C=C D(2+ 3 ), given array In E C F, 45^ = E C C F From Eq. (i) (H-h)(2+ 3 )=H+h array cc & H(2+ 3 )-h(2+ 3 )=H+h & H(1+ 3 )=h(3+ 3 ) & H=h ( 3+ 3 1+ 3 )=2500 ( 3+ 3 3 +1 ) & H=2500 3 ~m array

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