Question : $\triangle PQR$ is right-angled at $Q$. The length of $PQ$ is 5 cm and $\angle P R Q=30^{\circ}$. Determine the length of the side $QR$.
Option 1: $5 \sqrt{3}~cm$
Option 2: $3 \sqrt{3}~cm$
Option 3: $\frac{1}{\sqrt{3}}~cm$
Option 4: $\frac{5}{\sqrt{3}}~cm$
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Correct Answer: $5 \sqrt{3}~cm$
Solution :
$\angle PRQ$ = 30°
⇒ $\tan 30° = \frac{PQ}{QR}$
⇒ $\frac{1}{\sqrt3} = \frac{5}{QR}$
⇒ $QR = 5\sqrt{3}$ cm
Hence, the correct answer is $5\sqrt{3}~cm$.
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