Question

a right triangle has a leg of length 9 yards and a hypotenuse of length 40 yards. find the length of the other leg. provide an answer accurate to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the unknown leg be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a,b\) are the legs. Here \(a = 9\), \(c=40\), so \(x^{2}+9^{2}=40^{2}\).

Step2: Rearrange the equation

\(x^{2}=40^{2}-9^{2}\). Calculate \(40^{2}=1600\) and \(9^{2}=81\). Then \(x^{2}=1600 - 81=1519\).

Step3: Solve for \(x\)

\(x=\sqrt{1519}\approx38.97435\). Rounding to the nearest tenth, \(x\approx39.0\).

Answer:

\(39.0\) yards