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In a figure, PQR = 60^o, PRS = 90^o, RPS...

In a figure, PQR = 60^o, PRS = 90^o, RPS = 45^o, QR = 8cm. Determine PS

A.

2 $\sqrt{3}$ cm

B.

4 $\sqrt{6}$ cm

C.

2 $\sqrt{6}$ cm

D.

8 $\sqrt{6}$ cm

E.

8cm

View answer & explanation

Correct answer is B

From the diagram, sin 60^o = $\frac{PR}{8}$

PR = 8 sin 60 = $\frac{8\sqrt{3}}{2}$

= 4 $\sqrt{3}$

Cos 45^o = $\frac{PR}{PS}$ = $\frac{4 \sqrt{3}}{PS}$

PS Cos45^o = 4 $\sqrt{3}$

PS = 4 $\sqrt{3}$ x 2

= 4 $\sqrt{6}$

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