Question

select the correct answer. one leg of a right triangle is 10 units, and its hypotenuse is 12 units. what is the length of the other leg? a. about 7 units b. about 15 units c. about 25 units d. about 122 units e. about 224 units

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 10\), \(c=12\), and \(b\) be the unknown leg. The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), so \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 10\) and \(c = 12\) into the formula \(b^{2}=c^{2}-a^{2}\). We get \(b^{2}=12^{2}-10^{2}=144 - 100=44\).

Step3: Solve for \(b\)

\(b=\sqrt{44}\approx 6.63\approx7\) (rounded to the nearest whole - number).

Answer:

A. about 7 units