Chapter 10 - Exponents and Radicals - 10.7 The Distance Formula, the Midpoint Formula, and Other Applications - 10.7 Exercise Set - Page 676: 11

$a=8$

In the given right triangle, $a$ and $b$ are the legs and $c$ is the hypotenuse. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $ b=15 $ and $ c=17 ,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ a^2+15^2=17^2 \\\\ a^2+225=289 \\\\ a^2=289-225 \\\\ a^2=64 \\\\ a=\sqrt{64} \\\\ a=8 .\end{array}