Question : If $\triangle$PQR is right-angled at Q, PQ = 12 cm and $\angle$PRQ = 30°, then what is the value of QR?
Option 1: $12\sqrt{3}$
Option 2: $12\sqrt2$
Option 3: $12$
Option 4: $24$
Correct Answer: $12\sqrt{3}$
Solution :
$\triangle$ PQR is a right-angled at Q.
So, Hypotenuse is PR.
We know, tan $x$ = $\frac{\text{Opposite Side}}{\text{Adjacent Side}}$
tan($\angle$PRQ) = $\frac{PQ}{QR}$
⇒ tan 30° = $\frac{12}{QR}$
⇒ $\frac{1}{\sqrt{3}} = \frac{12}{QR}$
$\therefore$ QR = $12\sqrt{3}$ cm
Hence, the correct answer is $12\sqrt{3}$.
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