Answer
$17 \text{ } ft$
Work Step by Step
Let $x$ be the amount of cable needed. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, the conditions of the problem translate to
\begin{array}{l}\require{cancel}
15^2+8^2=x^2
\\
225+64=x^2
\\
289=x^2
\\
x=\sqrt{289}
\\
x=17
.\end{array}
Hence, the amount of cable needed, $x,$ is $
17 \text{ } ft
.$
