Question

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

Explanation:

Step1: Identify the theorem

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$ for right - triangles. Here, assume the two given sides are the legs of the right - triangle.

Step2: Substitute the values

Let $a = 6$ and $b = 8$. Then $c=\sqrt{a^{2}+b^{2}}=\sqrt{6^{2}+8^{2}}$.

Step3: Calculate

First, calculate $6^{2}=36$ and $8^{2}=64$. Then $a^{2}+b^{2}=36 + 64=100$. So $c=\sqrt{100}=10$.

Answer:

10