Answer
85 ft
Work Step by Step
Because the ceiling forms a 90-degree angle, we use the Pythagorean Theorem, $a^{2}+b^{2}=c^{2}$.
We are given the length of two sides, $a$ and $b$. $a=40$ feet and $b=75$ feet.
$40^{2}+75^{2}=c^{2}$
Now we must solve for $c^{2}$.
Evaluate the exponents: $1600+5625=7225$
$7225=c^{2}$
Solve for $c^{2}$.
$\sqrt 7225 = 85$
$85^{2}=7225$
$40^{2}+75^{2}=85^{2}$
Because $c=85$, the length of the speaker wire is $85$ ft.
