Question

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

Explanation:

Step1: Identify unknown as hypotenuse

Let the unknown side (hypotenuse) be $c$, the other sides are $a=6$, $b=\sqrt{11}$. Use Pythagorean theorem: $c^2 = a^2 + b^2$

Step2: Substitute values into formula

$$c^2 = 6^2 + (\sqrt{11})^2$$

Step3: Calculate each term

$$c^2 = 36 + 11$$

Step4: Sum and solve for $c$

$$c^2 = 47 \implies c = \sqrt{47}$$

Answer:

$\sqrt{47}$