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JEE Main20204 Sep 2020Evening ShiftMathematicsHeights and DistancesActual

The angle of elevation of a cloud C from a point P , 200 m above a still take is 30 o . If the angle of depression of the image of C in the lake from the point P is 60 o , then P C (in m ) is equal to

Options

  1. A100
  2. B200 3
  3. C400
  4. D400 3

Correct answer

C. 400

Step-by-step solution

tan 30 ° = x y = 1 3 ⇒ y = 3 x   and  tan 60 ° = x + 400 y So, x + 400 = 3 y = 3 x 2 x = 400 ,   x = 200 sin 30 ° = 200 PC ⇒ PC = 400

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