In the diagram, |QR| = 5cm, PQR = 60 o and PSR = 45 o
MATHEMATICS
WAEC 2006
In the diagram, |QR| = 5cm, PQR = 60o and PSR = 45o. Find |PS|, leaving your answer in surd form.
- A. 4\(\sqrt{5}\)cm
- B. 3\(\sqrt{7}\)cm
- C. 4\(\sqrt{6}\)cm
- D. 5\(\sqrt{6}\)cm
Correct Answer: D. 5\(\sqrt{6}\)cm
Explanation
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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