Answer
$3\sqrt{5} \text{ } ft.$
Work Step by Step
Using $a^2+b^2=c^2$ (or the Pythagorean Theorem) where the legs are given the measures $6$ feet and $3$ feet, then the hypotenuse, $c$, is equal to
\begin{array}{l}\require{cancel}
6^2+3^2=c^2
\\\\
36+9=c^2
\\\\
45=c^2
\\\\
c=\sqrt{45}
\\\\
c=\sqrt{9\cdot5}
\\\\
c=\sqrt{(3)^2\cdot5}
\\\\
c=3\sqrt{5}
.\end{array}
Hence, the unknown side is $
3\sqrt{5} \text{ } ft.
$