In the diagram, |QR| = 5cm, PQR = 60o and PSR = 45o. 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: Option D
Explanation
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