Question

the hypotenuse of a right triangle measures 4 cm and one of its legs measures 3 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 \(a = 3\), \(c = 4\), find \(b\). Rearrange formula: \(b=\sqrt{c^2 - a^2}\).

Step2: Substitute values

Substitute \(a = 3\), \(c = 4\) into formula: \(b=\sqrt{4^2 - 3^2}=\sqrt{16 - 9}=\sqrt{7}\).

Step3: Calculate and round

\(\sqrt{7}\approx2.6\) (rounded to nearest tenth).

Answer:

The measure of the other leg is approximately \(\boldsymbol{2.6}\) cm.