Question

find the length of the third side. if necessary, write in simplest radical form.
answer attempt 1 out of 2

Explanation:

Step1: Identify knowns and unknown

Let hypotenuse $c=6$, leg $a=3\sqrt{3}$, unknown leg $b$. Use Pythagorean theorem: $a^2 + b^2 = c^2$.

Step2: Rearrange to solve for $b$

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

Step3: Substitute values into formula

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

Step4: Simplify to find $b$

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

Answer:

3