In the diagram, |QR| = 10cm, PR⊥QS, angle PSR = 30^\circ and angle PQR = 45^\circ. Calculate in meters |QS|
Attached Figure / Diagram
A
\(10(1+\sqrt{3})\)
B
\(20\sqrt{3}\)
C
\(10\sqrt{3}\)
D
\((10+\sqrt{3})\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
In \(\Delta\) PQR,
\(\tan 45 = \frac{PR}{10} \implies PR = 10 \tan 45\)
= 10m
In \(\Delta\) PRS,
\(\tan 30 = \frac{10}{RS} \implies RS = \frac{10}{\tan 30}\)
= \(\frac{10}{\frac{1}{\sqrt{3}}\)
= \(10\sqrt{3}\)
PS = \(10 + 10\sqrt{3}\)
= \(10(1 + \sqrt{3}) cm\)
Source: Myschool Past Questions Archive (Record #26561)