Question

what is the length of the missing leg? if necessary, round to the nearest tenth.
a = square miles
(there is a right triangle in the picture, with one leg labeled 12 mi., the hypotenuse labeled 13 mi., and the other leg labeled a.)

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, $c^2 = a^2 + b^2$, where $c=13$, $b=12$. Rearrange to solve for $a$:
$a^2 = c^2 - b^2$

Step2: Substitute known values

$a^2 = 13^2 - 12^2 = 169 - 144$

Step3: Calculate and take square root

$a^2 = 25$, so $a = \sqrt{25}$

Answer:

5 miles