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JAMB Mathematics 1997 Question 37

Question 37

Trigonometry

In the figure above, XYZ is a triangle with XY = 5cm, XZ = 2cm and XZ is produced to E marking the angle YZE = 150°. If the angle XYZ = θ calculate the value of sin θ.

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

Answer: D (1/5)

Explanation

∠XZY = 180° − 150° = 30°. By the sine rule, sin θ/XZ = sin 30°/XY, so sin θ = 2 × ½ ÷ 5 = 1/5.