Question

in right triangle abc, angle c is a right angle, ab = 13 and bc = 5. what is the length of ac? ac =

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \(ABC\) with \(\angle C = 90^{\circ}\), by the Pythagorean theorem \(AB^{2}=AC^{2}+BC^{2}\). So, \(AC^{2}=AB^{2}-BC^{2}\).

Step2: Substitute the given values

Given \(AB = 13\) and \(BC = 5\). Then \(AC^{2}=13^{2}-5^{2}\).
Since \(13^{2}=169\) and \(5^{2}=25\), we have \(AC^{2}=169 - 25\).

Step3: Calculate \(AC^{2}\) and then \(AC\)

\(AC^{2}=144\). Taking the square root of both sides (since \(AC>0\) as it represents the length of a side of a triangle), \(AC=\sqrt{144}\).

Answer:

\(12\)