Chapter 9 - Section 9.1 - Solving Quadratic Equations by the Square Root Property - Exercise Set - Page 631: 41

$c=17 \text{ } m$

Using $a^2+b^2=c^2$ or the Pythagorean Theorem, then, \begin{array}{l}\require{cancel} 8^2+15^2=c^2 \\\\ 64+225=c^2 \\\\ 289=c^2 \\\\ c=\pm\sqrt{289} \\\\ c=\pm\sqrt{(17)^2} \\\\ c=\pm17 .\end{array} Since there are no negative measurements, then $ c=17 \text{ } m .$