Question

find the length of the third side. if necessary, round to the nearest tenth.

Explanation:

Step1: Identify the theorem

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse of a right - triangle. Here, assume the hypotenuse $c = 13$ and one side $a = 12$, and we want to find the other side $b$.

Step2: Rearrange the formula

We get $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute values

Substitute $c = 13$ and $a = 12$ into the formula: $b=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}$.

Step4: Calculate the result

$\sqrt{25}=5$.

Answer:

5