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Manipal MET2012MathematicsHeights and Distances

The height of the chimney when it is found that on walking towards it 50 m in the horizontal line through its base, the angle of elevation of its top changes from 30^ to 60^ , is

Options

  1. A25 3 ~m
  2. B25 m
  3. C25 4 ~m
  4. D25 3 ~m

Correct answer

A. 25 3 ~m

Step-by-step solution

Let P Q=h be the height of chimney. A and B are the two points 50 m apart. In A P Q , aligned 30^ & = h A P & A P =h 30^ ....(i) aligned and in Q B P , array rlrl & 60^ = h B P & B P =h 60^ ....(ii) & A P-B P =50 & h ( 30^ - 60^ )=50 h & = 50 ( 3 - 1 3 ) = 50 3 3-1 & = 50 3 2 =25 3 ~m array

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