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: Apply Pythagorean theorem

Let the sides of the right - triangle be $a = 4\sqrt{3}$, $b$ (the unknown side), and $c = 8$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$ (assuming $c$ is the hypotenuse). Then $b^{2}=c^{2}-a^{2}$.

Step2: Substitute values

Substitute $a = 4\sqrt{3}$ and $c = 8$ into the formula. $a^{2}=(4\sqrt{3})^{2}=4^{2}\times(\sqrt{3})^{2}=16\times3 = 48$, and $c^{2}=8^{2}=64$. So $b^{2}=64 - 48$.

Step3: Calculate $b^{2}$

$b^{2}=64 - 48=16$.

Step4: Find $b$

Take the square - root of both sides. Since $b>0$ (as it represents the length of a side of a triangle), $b=\sqrt{16}=4$.

Answer:

$4$