Which one of the following is <strong>CORRECT</strong>?
Consider the following for the next two (02) items that follow : 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. (Use the formula \tan 2\theta = \frac{2 \tan \theta}{1 - \tan^2 \theta})
- A. h^2=x^2-y^2
- B. h^2=x^2+y^2
- C. h^2=2(y^2-x^2)
- D. h^2=y^2-x^2 ✓
Correct Answer: D. h^2=y^2-x^2
Explanation
From the previous analysis, we established y = \sqrt{h^2+x^2} because \triangle RQT is isosceles. Squaring both sides yields y^2 = h^2 + x^2, which rearranges to h^2 = y^2 - x^2.
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