Question

question
one of the legs of a right triangle measures 1 cm and its hypotenuse measures 19 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 \(a = 1\), \(c = 19\), find \(b\).

Step2: Rearrange formula for \(b\)

\(b^2 = c^2 - a^2\)

Step3: Substitute values

\(b^2 = 19^2 - 1^2 = 361 - 1 = 360\)

Step4: Solve for \(b\)

\(b = \sqrt{360}\approx 18.9737\), round to nearest tenth: \(b\approx 19.0\)

Answer:

The measure of the other leg is approximately \(\boldsymbol{19.0}\) cm.