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

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

View answer & explanation

Correct answer is D

tan 6^o = $\frac{|PR|}{|QR|}$

$\sqrt{3} = \frac{|PR|}{5}$

= |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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