Question

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

Explanation:

Step1: Identify the problem type

This is a right - triangle problem, use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a,b$ are the legs.

Step2: Determine the values of $a$ and $b$

Let $a = 5$ and $b=12$. We want to find the hypotenuse $c$.

Step3: Apply the Pythagorean theorem

$c=\sqrt{a^{2}+b^{2}}=\sqrt{5^{2}+12^{2}}=\sqrt{25 + 144}=\sqrt{169}$.

Step4: Calculate the square - root

$\sqrt{169}=13$.

Answer:

13