Question

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

Explanation:

Step1: Apply Pythagorean theorem

Let the sides of the right - triangle be $a = \sqrt{7}$, $b$ (the unknown side), and $c = 3$. According to the Pythagorean theorem $c^{2}=a^{2}+b^{2}$, so $b^{2}=c^{2}-a^{2}$.

Step2: Substitute values

Substitute $a=\sqrt{7}$ and $c = 3$ into the formula $b^{2}=c^{2}-a^{2}$. We get $b^{2}=3^{2}-(\sqrt{7})^{2}=9 - 7$.

Step3: Calculate $b^{2}$ and $b$

$b^{2}=9 - 7=2$, then $b=\sqrt{2}$.

Answer:

$\sqrt{2}$