Question

one of the legs of a right triangle measures 12 cm and its hypotenuse measures 15 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 \(a = 12\), \(c = 15\), find \(b\). Rearrange formula: \(b=\sqrt{c^2 - a^2}\).

Step2: Substitute values

Substitute \(a = 12\), \(c = 15\) into formula: \(b=\sqrt{15^2 - 12^2}=\sqrt{225 - 144}=\sqrt{81}\).

Step3: Calculate square root

\(\sqrt{81}=9\), so the other leg is 9 cm.

Answer:

9 cm