In a right-angled triangle PQR, right-angled at Q, the length of the side PR is 17 units, length of the base QR is 8 units, and length of the side PQ is 15 units. If $\angle R P Q=\alpha$, then $\sin \alpha+\cos \alpha$ is:

$\frac{23}{17}$

We know that,

Sinθ = \(\frac{P}{H}\) 

Cosθ = \(\frac{B}{H}\) 

PR = 17

QR = 8

PQ = 15

sin α + cos α

= \(\frac{8}{17}\) + \(\frac{15}{17}\) 

= \(\frac{8 + 15}{17}\)  =\(\frac{23}{17}\)