Question

one of the legs of a right triangle measures 13 cm and its hypotenuse measures 17 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is hypotenuse, \(a\) and \(b\) are legs. Let one leg \(a = 13\), hypotenuse \(c = 17\), find \(b\). Rearrange formula: \(b=\sqrt{c^2 - a^2}\).

Step2: Substitute values

\(c^2=17^2 = 289\), \(a^2 = 13^2=169\). Then \(c^2 - a^2=289 - 169 = 120\).

Step3: Calculate square root

\(b=\sqrt{120}\approx10.954\), round to nearest tenth: \(11.0\).

Answer:

The measure of the other leg is approximately \(11.0\) cm.