Answer
$\sqrt{241} \text{ } ft$
Work Step by Step
Using $a^2+b^2=c^2$ (or the Pythagorean Theorem) with legs having measures $7$ and $8\sqrt{3}$, then the hypotenuse, $c$, is
\begin{array}{l}\require{cancel}
7^2+(8\sqrt{3})^2=c^2
\\\\
49+64\cdot3=c^2
\\\\
49+192=c^2
\\\\
241=c^2
\\\\
c=\sqrt{241}
.\end{array}
Hence the hypotenuse is $
\sqrt{241} \text{ } ft
.$
