Question

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

Explanation:

Step1: Recall Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$

Step2: Assign known values

Let $a=7$, $c=\sqrt{130}$, solve for $b$.

Step3: Rearrange formula for $b$

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

Step4: Substitute values and calculate

$b^2 = (\sqrt{130})^2 - 7^2 = 130 - 49 = 81$

Step5: Solve for $b$

$b = \sqrt{81} = 9$

Answer:

9