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TS EAMCET · Maths · Heights 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 \(45^{\circ}\) each. Then, the square of the distance between the tops of the poles is

  1. A \(\frac{a^2+b^2}{2}\)
  2. B \(a^2+b^2\)
  3. C \(2\left(a^2+b^2\right)\)
  4. D \(4\left(a^2+b^2\right)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(2\left(a^2+b^2\right)\)

Step-by-step Solution

Detailed explanation

In \(\triangle A P D\), \(\tan 45^{\circ}=\frac{a}{A P} \Rightarrow A P=a\) and in \(\triangle B P C\), \(\tan 45^{\circ}=\frac{b}{P B} \Rightarrow P B=b\) \(\therefore D E=a+b\) and \(C E=b-a\) In \(\triangle D E C\),…