Question

one of the legs of a right triangle measures 5 cm and its hypotenuse measures 13 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 5\), \(c = 13\), and \(b\) be the unknown leg. By Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), so \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 5\) and \(c = 13\) into \(b^{2}=c^{2}-a^{2}\). Then \(b^{2}=13^{2}-5^{2}=169 - 25=144\).

Step3: Solve for \(b\)

Take the square root of both sides. \(b=\sqrt{144}=12\)

Answer:

\(12\)