Question

question
the hypotenuse of a right triangle measures 4 cm and one of its legs measures 1 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 \(x\), hypotenuse \(c = 4\) cm and one leg \(a=1\) cm. Then we have \(1^{2}+x^{2}=4^{2}\).

Step2: Solve for \(x\)

First, simplify the equation: \(1 + x^{2}=16\). Subtract 1 from both sides: \(x^{2}=16 - 1=15\). Then take the square root of both sides: \(x=\sqrt{15}\approx3.9\) (rounded to the nearest tenth).

Answer:

The measure of the other leg is approximately \(\boldsymbol{3.9}\) cm.