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JAMB Mathematics 1979 Question 41

Question 41

Trigonometry

Find x in the diagram below: QR = 3, PS = x, <PQS = 30°, <PRS = 45°, <PSR = 90°

Diagram for this question
  1. A.3√3
  2. B.3(√3 − 1)/(√3 + 1)
  3. C.3/(√3 + 1)
  4. D.3/2(√3 − 1)
  5. E.3(√3 + 1)/2
Show the answer and explanation

Answer: E (3(√3 + 1)/2)

Explanation

With <PRS = 45°, RS = PS = x. In triangle PQS, tan 30° = x/(3 + x), so x√3 = 3 + x and x = 3/(√3 − 1) = 3(√3 + 1)/2.