Answer
$\text{approximately } 22.9 \text{ } m.$
Work Step by Step
Using $a^2+b^2=c^2$ (or the Pythagorean Theorem) where a leg is given the measure $9$ meters and the hypotenuse is given the measure $11\sqrt{5}$ meters, then the other leg, $b$, is equal to
\begin{array}{l}\require{cancel}
9^2+b^2=(11\sqrt{5})^2
\\\\
b^2=(11\sqrt{5})^2-9^2
\\\\
b^2=121\cdot5-81
\\\\
b^2=605-81
\\\\
b^2=524
\\\\
b=\sqrt{524}
\\\\
b\approx22.9
.\end{array}
Hence, the unknown side is $
\text{approximately } 22.9 \text{ } m.
$
