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Manipal MET2011MathematicsHeights and Distances

Each side of a square subtends an angle of 60^ at the top of a tower h metre high standing in the centre of the square. If a is the length of each side of the square, then

Options

  1. A2 a^2=h^2
  2. B2 h^2=a^2
  3. C3 a^2=2 h^2
  4. D2 h^2=3 a^2

Correct answer

C. 3 a^2=2 h^2

Step-by-step solution

Let A B C D be a square of each side of length a . It is given that O C P=60^ . Length of diagonal A C= a^2+a^2 =a 2 P C= A C 2 = a 2 In O C P, 60^ = O P P C array ll & 3 = h a / 2 & 3 a = 2 h & 3 a^2 =2 h^2 array

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