In the diagram, |QR| = 5cm, PQR = 60o and PSR = 45o. Find |PS|, leaving your answe in surd form.

  • A 4\(\sqrt{5}\)cm
  • B 3\(\sqrt{7}\)cm
  • C 4\(\sqrt{6}\)cm
  • D 5\(\sqrt{6}\)cm
waec 2006mathematics

The correct answer is D. 5\(\sqrt{6}\)cm

tan 6o = \(\frac{|PR|}{|QR|}\)

\(\sqrt{3} = \frac{|PR|}{5}\)

= |PR| = \(5 \sqrt{3}\)cm

sin 45 = \(\frac{|PR|}{|PS|}\)

\(\frac{1}{\sqrt{2}}\) = \(\frac{5 \sqrt{3}}{|PS|}\)

|PS| = \(5 \sqrt{3}\) x \(\sqrt{2}\)

= 5\(\sqrt{6}\)cm

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