Question

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

Explanation:

Step1: Identify Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $c=6$ (hypotenuse), $a=4$, $b$ is unknown side.

Step2: Rearrange to solve for $b$

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

Step3: Substitute given values

$b^2 = 6^2 - 4^2 = 36 - 16 = 20$

Step4: Simplify radical

$b = \sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$

Answer:

$2\sqrt{5}$