Question

the hypotenuse of a right triangle measures 15 cm and one of its legs measures 6 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 the hypotenuse and \(a\), \(b\) are the legs. Let the unknown leg be \(x\), hypotenuse \(c = 15\), one leg \(a=6\). So we have \(6^{2}+x^{2}=15^{2}\).

Step2: Solve for \(x^{2}\)

Calculate \(6^{2}=36\) and \(15^{2}=225\). Then \(x^{2}=225 - 36=189\).

Step3: Solve for \(x\)

Take the square root: \(x=\sqrt{189}\approx13.7\) (rounded to the nearest tenth).

Answer:

The measure of the other leg is approximately \(\boldsymbol{13.7}\) cm.