Question

in right triangle abc, angle c is a right angle, ab = 13, and bc = 12. what is the length of segment ac? ac = \boxed{} units

Explanation:

Step1: Recall Pythagorean theorem

In a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\), \(b\) are the legs. Here, \(AB\) is the hypotenuse (\(c = 13\)), \(BC\) is one leg (\(a = 12\)), and \(AC\) is the other leg (\(b\)). So the formula becomes \(AC^2+BC^2 = AB^2\), and we solve for \(AC\): \(AC=\sqrt{AB^2 - BC^2}\).

Step2: Substitute values into formula

Substitute \(AB = 13\) and \(BC = 12\) into the formula: \(AC=\sqrt{13^2 - 12^2}=\sqrt{169 - 144}=\sqrt{25}\).

Step3: Simplify the square root

\(\sqrt{25}=5\).

Answer:

\(5\)