Question

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

Explanation:

Step1: Identify the hypotenuse

The hypotenuse is the longest side of a right - triangle. Here, the hypotenuse $c = 20$ and one side $a = 16$.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse and $a,b$ are the other two sides. We want to find $b$, so $b=\sqrt{c^{2}-a^{2}}$.
Substitute $c = 20$ and $a = 16$ into the formula: $b=\sqrt{20^{2}-16^{2}}=\sqrt{(20 + 16)(20 - 16)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$).
First, calculate $(20 + 16)(20 - 16)=(36)\times(4)=144$.
Then, $b=\sqrt{144}=12$.

Answer:

12