In a right triangle, one leg measures $8yd$ and the hypotenuse measures $64yd$. What is the length of the other leg?

• A. $\sqrt{8^2-{64}^2}$
• B. $56yd$
• C. $\sqrt{{64}^2-8^2}=\sqrt{4032}=63.55yd$
• D. $72yd$

Answer: (C)

Verified step by step guidance

1. Identify the given sides of the right triangle: one leg is \(8\, yd\) and the hypotenuse is \(64\, yd\).
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (\(c\)) equals the sum of the squares of the legs (\(a\) and \(b\)): \(c^2 = a^2 + b^2\).
3. Assign the known values: let \(a = 8\, yd\), \(c = 64\, yd\), and \(b\) be the unknown leg length we want to find.
4. Rearrange the Pythagorean theorem to solve for the unknown leg \(b\): \(b = \sqrt{c^2 - a^2}\).
5. Substitute the known values into the formula: \(b = \sqrt{(64)^2 - (8)^2}\), then simplify under the square root to find the length of the other leg.