Question

find the length of the third side. if necessary, write in simplest radical form. 4 10 answer attempt 2 out of 2 21 submit answer

Explanation:

Step1: Identify Pythagorean theorem

We use $a^2 + b^2 = c^2$, where $c=10$ (hypotenuse), $a=4$, $b$ is unknown.

Step2: Rearrange to solve for $b$

$b^2 = c^2 - a^2$
$b^2 = 10^2 - 4^2$

Step3: Calculate the squares

$b^2 = 100 - 16 = 84$

Step4: Simplify the square root

$b = \sqrt{84} = \sqrt{4 \times 21} = 2\sqrt{21}$

Answer:

$2\sqrt{21}$