Question

what is the length of the missing leg? if necessary, round to the nearest tenth.
a = \square miles
(right triangle with one leg 1 mi, hypotenuse 3 mi, and the other leg a)

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle with hypotenuse $c$, legs $a$ and $b$, $a^2 + b^2 = c^2$. Here, $c=3$, $b=1$, so:
$$a^2 + 1^2 = 3^2$$

Step2: Simplify to solve for $a^2$

$$a^2 = 3^2 - 1^2 = 9 - 1 = 8$$

Step3: Calculate $a$ and round

$$a = \sqrt{8} \approx 2.8$$

Answer:

2.8 miles