In the diagram, |QR| = 5cm, PQR = 60o and PSR = 45o. Find |PS|, leaving your answe in surd form.
- 4\(\sqrt{5}\)cm
- 3\(\sqrt{7}\)cm
- 4\(\sqrt{6}\)cm
-
5\(\sqrt{6}\)cm
The correct answer is: D
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