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WAEC Mathematics 2002 Question 41

Question 41

Trigonometry

In the diagram, |QR| = 10cm, PR ⊥ QS, angle PSR = 30° and angle PQR = 45°. Calculate in metres, |QS|.

Diagram for this question
  1. A.10(1 + √3)
  2. B.20√3
  3. C.10√3
  4. D.(10 + √3)
Show the answer and explanation

Answer: A (10(1 + √3))

Explanation

Angle Q = 45°, so PR = QR = 10. In triangle PRS, RS = PR/tan 30° = 10√3. QS = 10 + 10√3 = 10(1 + √3).