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. Here, assume the hypotenuse $c = 7$ and one - side $a = 4$, and we want to find the other side $b$.

Step2: Rearrange the formula

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

Step3: Substitute values

$b=\sqrt{7^{2}-4^{2}}=\sqrt{49 - 16}=\sqrt{33}$.

Step4: Calculate and round

$\sqrt{33}\approx5.7$.

Answer:

$5.7$