Question

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

Explanation:

Step1: Identify the sides and the Pythagorean theorem

Let the two given sides be $a = 3$ and $c=7$. Assume the unknown side is $b$. For a right - triangle, the Pythagorean theorem is $a^{2}+b^{2}=c^{2}$ (where $c$ is the hypotenuse). Here, since $7>3$, $7$ is the hypotenuse.

Step2: Rearrange the Pythagorean theorem to solve for $b$

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

Step3: Simplify and round

$\sqrt{40}\approx6.3$ (rounded to the nearest tenth).

Answer:

$6.3$