Question

the hypotenuse of a right triangle measures 15 cm and one of its legs measures 6 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 \(c = 15\), \(a = 6\), find \(b\). Rearrange formula: \(b=\sqrt{c^2 - a^2}\).

Step2: Substitute values

Substitute \(c = 15\) and \(a = 6\) into formula: \(b=\sqrt{15^2 - 6^2}=\sqrt{225 - 36}=\sqrt{189}\).

Step3: Simplify and round

\(\sqrt{189}\approx13.7\) (rounded to nearest tenth).

Answer:

\(13.7\) cm