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 $c = 10$ and one - side $a = 6$.

Step2: Rearrange the formula

We want to find the other side $b$. Rearranging gives $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute values

Substitute $c = 10$ and $a = 6$ into the formula: $b=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}$.

Step4: Calculate the result

$\sqrt{64}=8$.

Answer:

8