Question

a right triangle has a leg of length 22 yards and a hypotenuse of length 38 yards. find the length of the other leg. provide an answer accurate to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 22\), \(c=38\), and \(b\) be the unknown leg. By \(a^{2}+b^{2}=c^{2}\), we get \(b^{2}=c^{2}-a^{2}\).
Substitute values: \(b^{2}=38^{2}-22^{2}\).
Calculate \(38^{2}=1444\), \(22^{2} = 484\). Then \(b^{2}=1444 - 484=960\).

Step2: Solve for \(b\)

\(b=\sqrt{960}\approx30.98386677\).
Round to the nearest tenth: \(b\approx31.0\).

Answer:

\(31.0\) yards