Question

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

Explanation:

Step1: Identify Pythagorean theorem

For right triangle: $c^2 = a^2 + b^2$, where $c=6$, $a=3\sqrt{3}$, solve for $b$.

Step2: Rearrange to solve for $b$

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

Step3: Substitute known values

$b^2 = 6^2 - (3\sqrt{3})^2 = 36 - 27$

Step4: Simplify and solve for $b$

$b^2 = 9$, so $b = \sqrt{9} = 3$

Answer:

3