Question

what is the length of the missing leg? if necessary, round to the nearest tenth.
b = square miles
(the image shows a right triangle with one leg 6 mi, hypotenuse 10 mi, and the other leg labeled b)

Explanation:

Step1: Recall Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $c=10$, $a=6$

Step2: Rearrange to solve for $b$

$b^2 = c^2 - a^2$

Step3: Substitute known values

$b^2 = 10^2 - 6^2 = 100 - 36 = 64$

Step4: Calculate square root of 64

$b = \sqrt{64} = 8$

Answer:

8 miles