Question

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

Step1: Identify Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $c=8$, $a=4\sqrt{3}$, solve for $b$.

Step2: Rearrange formula to solve for $b$

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

Step3: Substitute known values

$b^2 = 8^2 - (4\sqrt{3})^2 = 64 - (16\times3) = 64 - 48$

Step4: Calculate and simplify $b$

$b^2 = 16$, so $b = \sqrt{16} = 4$

Answer:

4