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 $c=5$, $a=\sqrt{21}$, solve for $b$.

Step2: Rearrange to solve for $b$

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

Step3: Substitute known values

$b^2 = 5^2 - (\sqrt{21})^2 = 25 - 21 = 4$

Step4: Take square root of $b^2$

$b = \sqrt{4} = 2$

Answer:

2