Question

what is the missing side length of this right triangle? type the answer in the box 5 in. 13 in.

Explanation:

Step1: Identify the formula

For a right triangle, we use the Pythagorean theorem: \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse, and \(a\), \(b\) are the legs. Here, hypotenuse \(c = 13\) in, one leg \(a = 5\) in, and we need to find the other leg \(b\). Rearranging the formula for \(b\): \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

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

Step3: Calculate the square root

\(\sqrt{144}=12\).

Answer:

12 inches