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

Explanation:

Step1: Identify the theorem

Use Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here $c = 10$ and $a = 5$, we need to find $b$.

Step2: Rearrange the formula

$b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute values

$b=\sqrt{10^{2}-5^{2}}=\sqrt{100 - 25}=\sqrt{75}$.

Step4: Simplify the radical

$\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}$.

Answer:

$5\sqrt{3}$