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WAEC Mathematics 2006 Question 13

Question 13

Trigonometry

In the diagram, |QR| = 5 cm, PQ̂R = 60° and PŜR = 45°. Find |PS|, leaving your answer in surd form.

Diagram for this question
  1. A.4√5 cm
  2. B.3√7 cm
  3. C.4√6 cm
  4. D.5√6 cm
Show the answer and explanation

Answer: D (5√6 cm)

Explanation

In right triangle PQR, |PR| = 5 tan 60° = 5√3. In right triangle PRS, |PS| = |PR| ÷ sin 45° = 5√3 × √2 = 5√6 cm.