Question

16 multiple choice 2 points
triangle abc is a right triangle. which equation could be used to determine the length of side ac?
a
x
15
c
8
b
x = \sqrt{8^{2}+15^{2}}
x = 8^{2}+15^{2}
x = 15^{2}-8^{2}
x = \sqrt{15^{2}-8^{2}}

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, hypotenuse \(AB = 15\), \(BC=8\), and \(AC=x\). So \(x^{2}+8^{2}=15^{2}\), then \(x^{2}=15^{2}-8^{2}\).

Step2: Solve for \(x\)

Take square root on both sides: \(x=\sqrt{15^{2}-8^{2}}\).

Answer:

\(x = \sqrt{15^{2}-8^{2}}\) (the fourth option)