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, $c = 21$ and one leg $a = 13$.

Step2: Rearrange the formula

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

Step3: Substitute values

$b=\sqrt{21^{2}-13^{2}}=\sqrt{(21 + 13)(21 - 13)}=\sqrt{34\times8}=\sqrt{272}$.

Step4: Calculate the square - root

$\sqrt{272}\approx16.5$.

Answer:

$16.5$