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JAMB Mathematics 1983 Question 20

Question 20

Trigonometry

PQRS is a desk of dimensions 2m × 0.8m which is inclined at 30° to the horizontal. Find the inclination of the diagonal PR to the horizontal.

Diagram for this question
  1. A.23°35'
  2. B.30°
  3. C.15°36'
  4. D.10°
  5. E.10°42'.
Show the answer and explanation

Answer: E (10°42'.)

Explanation

The 0.8m edge rises at 30°, so R is 0.8 sin 30° = 0.4m higher than P. The diagonal is √(2² + 0.8²) ≈ 2.154m, so sin θ = 0.4/2.154 ≈ 0.186 and θ ≈ 10°42'.