In the diagram, |QR| = 5cm, PQR = 60o and PSR = 45o. Find |PS|, leaving your answe in surd form.
Attached Figure / Diagram
A
4\(\sqrt{5}\)cm
B
3\(\sqrt{7}\)cm
C
4\(\sqrt{6}\)cm
D
5\(\sqrt{6}\)cm
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #36203)