Question

find the length of the third side. if necessary, write in simplest radical form. $3\sqrt{5}$ 9

Explanation:

Step1: Identify Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $c=9$, $a=3\sqrt{5}$, $b$ is unknown.

Step2: Rearrange to solve for $b^2$

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

Step3: Substitute known values

$b^2 = 9^2 - (3\sqrt{5})^2 = 81 - (9\times5) = 81 - 45$

Step4: Calculate and simplify $b$

$b^2 = 36$, so $b = \sqrt{36} = 6$

Answer:

6