Question

$△PQR$, right-angled at Q, if PR = 24 cm, QR = 12 cm, then find the value of $\angle QRP$.

• A. 30^o
• B. 60^o
• C. 45^o
• D. 90^o

Answer 1

The correct option is B

60^o

Given: PQR is aright angled triangle, right angled at Q and PR = 24 cm, QR = 12 cm.

In $△$PQR,
$sinP=\frac{QR}{PR}=\frac{12}{24}$
Since, $sin{30}^o=0.5$
We have $\angle RPQ={30}^o$

For a triangle, sum of all the angles =${180}^o$
$\Rightarrow \angle PQR+\angle QRP+\angle RPQ={180}^o$
$\Rightarrow {90}^o+\angle QRP+{30}^o={180}^o$
$\Rightarrow \angle QRP={180}^o-{120}^o={60}^o$
$\Rightarrow \angle QRP={60}^o$
Hence the correct answer is option B.