Question

there is a right triangle with one leg labeled 8 mi, the hypotenuse labeled 16 mi, and the other leg labeled x. the options are: a) $8\sqrt{3}$ miles, b) $16\sqrt{2}$ miles, c) $8\sqrt{2}$ miles, d) $16\sqrt{3}$ miles.

Explanation:

Step1: Apply Pythagorean theorem

$x^2 + 8^2 = 16^2$

Step2: Calculate squares

$x^2 + 64 = 256$

Step3: Solve for $x^2$

$x^2 = 256 - 64 = 192$

Step4: Find square root of $x^2$

$x = \sqrt{192} = 8\sqrt{3}$

Answer:

A. $8\sqrt{3}$ miles