Question

1. find the length of the third side. if necessary, write your answer in the simplest radical form.

5
9

Explanation:

Step1: Identify the hypotenuse

The hypotenuse is the longest side of a right - triangle. Here, assume the hypotenuse $c = 9$ and one leg $a = 5$. We use the Pythagorean theorem $c^{2}=a^{2}+b^{2}$, and we want to find $b$.

Step2: Rearrange the Pythagorean theorem

We can rewrite the Pythagorean theorem to solve for $b$ as $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute the values

Substitute $a = 5$ and $c = 9$ into the formula: $b=\sqrt{9^{2}-5^{2}}=\sqrt{81 - 25}=\sqrt{56}$.

Step4: Simplify the radical

We simplify $\sqrt{56}=\sqrt{4\times14}=2\sqrt{14}$.

Answer:

$2\sqrt{14}$