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

In the diagram, |QR| = 5cm, PQR = 60<sup>o</sup> and PSR = 45<sup>o</sup>. 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

Correct answer is D

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