Question

1. given a right triangle with a leg of 6 feet and hypotenuse of length 10 feet, find the length of the unknown leg.

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 \(a = 6\), \(c = 10\), find \(b\).

Step2: Rearrange formula for \(b\)

\(b^2 = c^2 - a^2\)

Step3: Substitute values

\(b^2 = 10^2 - 6^2 = 100 - 36 = 64\)

Step4: Solve for \(b\)

\(b = \sqrt{64} = 8\)

Answer:

The length of the unknown leg is 8 feet.