A wire is stretched from the top of an 8-ft pole to a bracket 5ft. from the base of the pole. How long is the wire?

For this question, you can use the Pythagorean Theorem: $${{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$ since this is a right triangle. A and b are the legs (shorter sides) of the triangle and c is the hypotenuse (longest side, diagonal side).

a  and b are 8 and 5 since the length of the wire is the diagonal side of the right triangle. So set up the equation:

$${{\mathtt{8}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{5}}}^{{\mathtt{2}}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$

Simplify the left side:

64 + 25 = c²

89 = c²

Now take the square root of both sides:

$${\sqrt{{\mathtt{89}}}} = {\mathtt{9.433\: \!981\: \!132\: \!056\: \!603\: \!8}}$$  = c

So the wire is about 9.434 or 9.4 feet long.