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. x=y
- B. x \lt y ✓
- C. x \gt y
- D. Cannot be concluded due to insufficient data
Correct Answer: B. x \lt y
Explanation
Let the top of the tower be T. The external angle of \triangle RQT is \angle TQP = 2\theta. Since \angle TRQ = \theta, we have \angle RTQ = \theta. Thus, \triangle RQT is isosceles with RQ = QT. Since QT = \sqrt{h^2+x^2}, we get y = \sqrt{h^2+x^2}. Since h > 0, it implies y \gt x, or x \lt y.
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