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 and $a$ and $b$ are the legs. Here, assume the two given sides are the legs of the right - triangle.

Step2: Substitute values

Let $a = 3$ and $b = 5$. Then $c=\sqrt{a^{2}+b^{2}}=\sqrt{3^{2}+5^{2}}=\sqrt{9 + 25}=\sqrt{34}$.

Step3: Calculate and round

$\sqrt{34}\approx5.8$

Answer:

$5.8$