Question

question
the hypotenuse of a right triangle measures 6 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 \(a = 3\), \(c = 6\), find \(b\).

Step2: Rearrange formula for \(b\)

\(b=\sqrt{c^{2}-a^{2}}\)

Step3: Substitute values

\(b = \sqrt{6^{2}-3^{2}}=\sqrt{36 - 9}=\sqrt{27}\approx5.2\) (rounded to nearest tenth)

Answer:

The measure of the other leg is approximately \(5.2\) cm.