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

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

Answer Details

From the diagram, sin 60o = $\frac{PR}{8}$
PR = 8 sin 60 = $\frac{8\sqrt{3}}{2}$
= 4$\sqrt{3}$
Cos 45o = $\frac{PR}{PS}$ = $\frac{4\sqrt{3}}{PS}$
PS Cos45o = 4$\sqrt{3}$
PS = 4$\sqrt{3}$ x 2
= 4$\sqrt{6}$