Question

one of the legs of a right triangle measures 11 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, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\), \(b\) are the legs. Let one leg \(a = 11\) cm, hypotenuse \(c=17\) cm, and the other leg be \(b\). We need to solve for \(b\), so we can rearrange the formula to \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

Substitute \(a = 11\) and \(c = 17\) into the formula: \(b=\sqrt{17^{2}-11^{2}}\). First, calculate \(17^{2}=289\) and \(11^{2} = 121\). Then, \(17^{2}-11^{2}=289 - 121=168\). So, \(b=\sqrt{168}\).

Step3: Calculate the square root and round

\(\sqrt{168}\approx12.961\), and rounding to the nearest tenth gives \(13.0\).

Answer:

The measure of the other leg is approximately \(13.0\) cm.