Question

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

Explanation:

Step1: Identify the formula

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$ for a right - triangle, where $c$ is the hypotenuse and $a$, $b$ are the legs. Here, if the two given sides are legs, and we want to find the hypotenuse. Let $a = 6$ and $b=10$.

Step2: Apply the Pythagorean theorem

$c=\sqrt{a^{2}+b^{2}}=\sqrt{6^{2}+10^{2}}=\sqrt{36 + 100}=\sqrt{136}$.

Step3: Simplify and round

$\sqrt{136}\approx11.7$.

Answer:

$11.7$