Question

find the length of the third side of the right triangle. the length of the third side is . (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, $c = 13$ and $a = 5$. We want to find $b$. So, $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $c = 13$ and $a = 5$ into the formula: $b=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}$.

Step3: Simplify the square - root

$\sqrt{144}=12$.

Answer:

12