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 states that \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs. Let the unknown leg be \(x\). We know \(c = 16\) and one leg (say \(a=11\)), so we can rewrite the formula as \(x^{2}+11^{2}=16^{2}\).

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

First, calculate \(11^{2}=121\) and \(16^{2}=256\). Then, \(x^{2}=256 - 121\). So \(x^{2}=135\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{135}\). Simplify \(\sqrt{135}=\sqrt{9\times15}=3\sqrt{15}\approx3\times3.87298\approx11.6\) (rounded to the nearest tenth).

Answer:

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