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JAMB Mathematics 1982 Question 4

Question 4

Trigonometry

In the above diagram, angle QPR = 90°, angle PSR = 90° and PR = 5 units. Find the length of QS.

Diagram for this question
  1. A.5 tan 25° sin 65°
  2. B.5 cot 25° sin 65°
  3. C.5 tan 25° cos 65°
  4. D.5 cot 25° cos 65°
  5. E.5 cosec 25°.
Show the answer and explanation

Answer: B (5 cot 25° sin 65°)

Explanation

In triangle PQR, <R = 65°, so PS = PR sin 65° = 5 sin 65°. In triangle PQS, tan 25° = PS/QS, so QS = 5 sin 65°/tan 25° = 5 cot 25° sin 65°.