Question : $\triangle PQR$ is right angled at Q. If $m\angle R=60^{\circ}$, what is the length of PR(in cm), If RQ = $4\sqrt3$ cm?
Option 1: $8$
Option 2: $4$
Option 3: $\frac{8}{\sqrt3}$
Option 4: $8\sqrt3$
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Correct Answer: $8\sqrt3$
Solution :
In $\triangle$PQR,
$\cos R$ = $\frac{QR}{PR}$
$\cos 60^{\circ}$ = $\frac{\text{Base}}{\text{Hypotenuse}}$
⇒ $\frac{1}{2}$ = $\frac{4\sqrt3}{x}$
⇒ $x$ = $8\sqrt3$
⇒ PR = $8\sqrt3$ cm
Hence, the correct answer is $8\sqrt3$.
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