Question

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

Explanation:

Step1: Identify the problem type

This is a right - triangle problem. Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse (the longest side) and $a$ and $b$ are the other two sides. Here, assume the hypotenuse $c = 13$ and one side $a = 9$, and we want to find the other side $b$.

Step2: Rearrange the Pythagorean theorem

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

Step3: Substitute the values

Substitute $c = 13$ and $a = 9$ into the formula: $b=\sqrt{13^{2}-9^{2}}=\sqrt{169 - 81}=\sqrt{88}$.

Step4: Calculate the value

$\sqrt{88}\approx9.4$.

Answer:

$9.4$