#### Answer

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

#### Work Step by Step

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
.$