Question

what is the missing side length of this right triangle? type the answer in the box. image of a right triangle with one leg labeled 5 in, hypotenuse labeled 13 in, right angle at the bottom - left corner inches

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is hypotenuse, \(a,b\) are legs. Let missing side be \(x\), hypotenuse \(c = 13\), one leg \(b = 5\), so \(x^2 + 5^2 = 13^2\).

Step2: Solve for \(x^2\)

\(x^2 = 13^2 - 5^2 = 169 - 25 = 144\).

Step3: Find \(x\)

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

Answer:

12