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2023 · Q34

AB is a straight road leading to the foot P of a tower of height h. Q is at distance x from P and R is at a distance y from Q (R is farther from P than Q; R, Q are on the same side). The angle of elevation of the top of the tower at Q is twice of that at R. Which one of the following is correct?

Elementary MathematicsTrigonometry
  1. Ah = √(x² − y²)/2
  2. Bh = √(x² + y²)/2
  3. Ch = √(2(y² − x²))/2
  4. Dh = √(y² − x²)/2

Explanation

With angle theta at R and 2theta at Q: tan2theta=h/x, tantheta=h/(x+y); eliminating theta gives h^2=y^2-x^2, which matches none of the options exactly as printed. Keyed option (d). Key disputed: verify against the official UPSC key.