In the diagram, QR = 10cm, PR⊥QS, angle PSR = 30° and angle PQR = 45°. Calculate in meters QS

A.
(10(1+sqrt{3})) 
B.
(20sqrt{3}) 
C.
(10sqrt{3}) 
D.
((10+sqrt{3}))
Correct Answer: Option A
Explanation
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}})
= (10sqrt{3})
PS = (10 + 10sqrt{3})
= (10(1 + sqrt{3}) cm)