Question

the hypotenuse of a right triangle measures 10 cm and one of its legs measures 7 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle with legs \(a\), \(b\) and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Let the unknown leg be \(x\), one leg \(a = 7\) cm, hypotenuse \(c=10\) cm. So we have \(7^{2}+x^{2}=10^{2}\).

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

Calculate \(7^{2}=49\) and \(10^{2} = 100\). Then the equation becomes \(49+x^{2}=100\). Subtract 49 from both sides: \(x^{2}=100 - 49=51\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{51}\approx7.1\) (rounded to the nearest tenth).

Answer:

The measure of the other leg is approximately \(7.1\) cm.