In a figure, PQR = 60o, PRS = 90o, RPS = 45o, 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
Correct Answer: Option B
Explanation
From the diagram, sin 60o = (frac{PR}{8})
PR = 8 sin 60 = (frac{8sqrt{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})