Question

what is the length of the hypotenuse? if necessary, round to the nearest tenth.
$c = \square$ miles

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, $c^2 = a^2 + b^2$, where $a=12$, $b=9$.

$$\begin{align*} c^2 &= 12^2 + 9^2 \end{align*}$$

Step2: Calculate squared side lengths

Compute $12^2$ and $9^2$, then sum.

$$\begin{align*} c^2 &= 144 + 81 = 225 \end{align*}$$

Step3: Solve for hypotenuse $c$

Take square root of 225.

$$\begin{align*} c &= \sqrt{225} = 15 \end{align*}$$

Answer:

15 miles