Question

1. what is the length of the unknown leg of the right triangle rounded to the nearest tenth of a foot? 2 ft 9 ft

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is hypotenuse, \(a\) and \(b\) are legs. Let the unknown leg be \(x\), one leg \(a = 2\), hypotenuse \(c=9\). So \(2^{2}+x^{2}=9^{2}\).

Step2: Solve for \(x\)

\(x^{2}=9^{2}-2^{2}=81 - 4 = 77\). Then \(x=\sqrt{77}\approx8.8\) (rounded to nearest tenth).

Answer:

\(8.8\) feet