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JAMB Mathematics 1993 Question 40

Question 40

Trigonometry

From the figure above, calculate TH in centimetres

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

Answer: B (5/(√3 − 1))

Explanation

Let TH = h. The 45° angle at Q makes QH = h, so PH = 5 + h. Then tan 30° = h/(5 + h), i.e. 5 + h = h√3, so h = 5/(√3 − 1).