Question

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

Explanation:

Step1: Identify the hypotenuse

The hypotenuse $c = 6$, and one - side $a=\sqrt{11}$. Let the third side be $b$.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. Rearranging for $b$, we get $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute the values

Substitute $c = 6$ and $a=\sqrt{11}$ into the formula: $b=\sqrt{6^{2}-(\sqrt{11})^{2}}=\sqrt{36 - 11}$.

Step4: Simplify the expression

$\sqrt{36 - 11}=\sqrt{25}=5$.

Answer:

$5$