Question

the hypotenuse of a right triangle measures 16 cm and one of its legs measures 11 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs. Let the unknown leg be \(x\), the known leg \(a = 11\) cm, and hypotenuse \(c=16\) cm. Then we have \(11^{2}+x^{2}=16^{2}\).

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

First, calculate \(11^{2}=121\) and \(16^{2} = 256\). Then the equation becomes \(121+x^{2}=256\). Subtract 121 from both sides: \(x^{2}=256 - 121=135\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{135}\). Simplify \(\sqrt{135}=\sqrt{9\times15} = 3\sqrt{15}\approx3\times3.873\approx11.6\) (rounded to the nearest tenth).

Answer:

The measure of the other leg is approximately \(\boldsymbol{11.6}\) cm.