Question : In a right-angled triangle PQR, right-angled at Q, the length of the side PR is 17 units, the length of the base QR is 8 units, and the length of the side PQ is 15 units. If $\angle RPQ = \sin\alpha $, then $\sin\alpha + \cos\alpha$ is:
Option 1: $\frac{18}{17}$
Option 2: $\frac{23}{17}$
Option 3: $\frac{21}{17}$
Option 4: $\frac{15}{17}$
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Correct Answer: $\frac{23}{17}$
Solution :
Given, triangle PQR is right-angled at Q with $\angle$RPQ = $\alpha$
PR is 17 units, QR = 8 units, and PQ = 15 units
$\sin\alpha+\cos\alpha$
= $\frac{\text{QR}}{\text{PR}}+\frac{\text{PQ}}{\text{PR}}$
= $\frac{8}{17}+\frac{15}{17}$
= $\frac{23}{17}$
Hence, the correct answer is $\frac{23}{17}$.
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