Question

what is the missing side length of this right triangle? type the answer in the box.

Explanation:

Step1: Identify the Pythagorean theorem

For a right - triangle with sides $a$, $b$ and hypotenuse $c$, $a^{2}+b^{2}=c^{2}$. Here, if the hypotenuse $c = 13$ in and one side $a = 5$ in, and we want to find the other side $b$. We can rewrite the formula as $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute the values

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

Step3: Calculate the square - root

$\sqrt{144}=12$.

Answer:

12 in.