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AP EAMCET2009MathematicsHeights and Distances

P is a point on the segment joining the feet of two vertical poles of heights a and b . The angles of elevation of the tops of the poles from P are 45^ each. Then, the square of the distance between the tops of the poles is

Options

  1. Aa^2+b^2 2
  2. Ba^2+b^2
  3. C2 (a^2+b^2 )
  4. D4 (a^2+b^2 )

Correct answer

C. 2 (a^2+b^2 )

Step-by-step solution

In A P D , 45^ = a A P A P=a and in B P C , 45^ = b P B P B=b D E=a+b and C E=b-a In D E C , aligned D C^2 & =D E^2+E C^2 & =(a+b)^2+(b-a)^2 & =2 (a^2+b^2 ) aligned

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