Question

what is the length of the missing leg? if necessary, round to the nearest tenth. a = centimeters

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, \(c = 13\) cm and one leg \(b = 12\) cm. We want to find \(a\), so \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

Substitute \(c = 13\) and \(b = 12\) into the formula: \(a=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}\).

Step3: Calculate the square - root

\(\sqrt{25}=5\)

Answer:

5