Chapter 9 - Section 9.1 - Solving Quadratic Equations by the Square Root Property - Exercise Set - Page 632: 47

$b=5\sqrt{7} \text{ } m$

Using $a^2+b^2=c^2$ or the Pythagorean Theorem, then, \begin{array}{l}\require{cancel} 9^2+b^2=16^2 \\\\ 81+b^2=256 \\\\ b^2=256-81 \\\\ b^2=175 \\\\ b=\pm\sqrt{175} \\\\ b=\pm\sqrt{25\cdot7} \\\\ b=\pm\sqrt{(5)^2\cdot7} \\\\ b=\pm5\sqrt{7} .\end{array} Since there are no negative measurements, then $ b=5\sqrt{7} \text{ } m .$