In the diagram above, PR is perpendicular from P to QS, PQ = 2cm, QR = 1cm and PR = RS. what is the size of the angle QPS?

  • A 135o
  • B 105o
  • C 90o
  • D 75o
  • E 60o
waec 1988mathematics

The correct answer is D. 75o

\(\Delta RPS\) = Isosceles triangle

\(\therefore < RPS = \​​​​​​​frac{180° - 90°}{2}\)

= 45°

In \(\Delta QPR\),\(\sin < QPR = \frac{1}{2}\)

= 30°

\(\therefore < QPS = 30° + 45° = 75°\)

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