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: $\frac{15}{17}$

Question

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: $\frac{15}{17}$

Team Careers360 · Accepted Answer

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
$\sin\alpha+\cos\alpha$
= $\frac{ ext{QR}}{ ext{PR}}+\frac{ ext{PQ}}{ ext{PR}}$
= $\frac{8}{17}+\frac{15}{17}$
= $\frac{23}{17}$
Hence, the correct answer is $\frac{23}{17}$.

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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 ∠RPQ=sin⁡α, then sin⁡α+cos⁡α is:Option 1: 1817Option 2: 2317Option 3: 2117Option 4: 1517

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