Question

the hypotenuse of a right triangle measures 5 cm and one of its legs measures 4 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 \(a\), \(b\) are the legs. Let the unknown leg be \(x\), \(c = 5\), one leg \(a=4\). So we have \(4^{2}+x^{2}=5^{2}\).

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

Calculate \(4^{2}=16\) and \(5^{2}=25\). Then the equation becomes \(16 + x^{2}=25\). Subtract 16 from both sides: \(x^{2}=25 - 16=9\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a leg, we take the positive square root. So \(x=\sqrt{9} = 3\).

Answer:

The measure of the other leg is \(\boldsymbol{3}\) cm.