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 $c=\sqrt{130}$, $b=7$, find $a$.

Step2: Rearrange to solve for $a$

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

Step3: Substitute known values

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

Step4: Calculate and simplify

$a^2 = 81$, so $a = \sqrt{81} = 9$

Answer:

9