Question

find the length of the third side. if necessary, write in simplest radical form.

Explanation:

Step1: Identify Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $c=9$, $b=\sqrt{17}$, $a$ is unknown leg.

Step2: Rearrange to solve for $a^2$

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

Step3: Substitute known values

$a^2 = 9^2 - (\sqrt{17})^2 = 81 - 17$

Step4: Calculate and simplify $a$

$a^2 = 64$, so $a = \sqrt{64} = 8$

Answer:

8