Question

one of the legs of a right triangle measures 17 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 with legs \(a\), \(b\) and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Let one leg \(a = 17\) cm, hypotenuse \(c=19\) cm, and the other leg be \(b\). We need to solve for \(b\). Rearranging the formula for \(b\), we get \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

Substitute \(a = 17\) and \(c = 19\) into the formula: \(b=\sqrt{19^{2}-17^{2}}\). First, calculate \(19^{2}=361\) and \(17^{2}=289\). Then, \(19^{2}-17^{2}=361 - 289=72\). So, \(b=\sqrt{72}\).

Step3: Simplify and round

Simplify \(\sqrt{72}\approx8.485\). Rounding to the nearest tenth, we look at the hundredth place (8). Since \(8\geq5\), we round up the tenth place. So, \(8.485\approx8.5\).

Answer:

The measure of the other leg is approximately \(8.5\) cm.