Question

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

Explanation:

Step1: Identify the triangle type

It's a right - triangle. Let the two given sides be $a = 3$ and $c=7$, and the unknown side be $b$.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$ (where $c$ is the hypotenuse). We need to solve for $b$. Rearranging the formula gives $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute values

Substitute $a = 3$ and $c = 7$ into the formula: $b=\sqrt{7^{2}-3^{2}}=\sqrt{49 - 9}=\sqrt{40}$.

Step4: Simplify and round

$\sqrt{40}\approx6.3$.

Answer:

$6.3$