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 Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$, $b$ are the legs.

Step2: Substitute values

Let $a = 18$ and $b = 24$. We want to find the hypotenuse $c$. So $c=\sqrt{a^{2}+b^{2}}=\sqrt{18^{2}+24^{2}}$.

Step3: Calculate squares

$18^{2}=324$ and $24^{2}=576$. Then $a^{2}+b^{2}=324 + 576=900$.

Step4: Calculate the square - root

$c=\sqrt{900}=30$.

Answer:

30