1. **State the problem:** We need to determine if a triangle with side lengths 40 yards, 42 yards, and 58 yards is a right triangle. 2. **Recall the converse of the Pythagorean theorem:** A triangle is right-angled if and only if the square of the longest side equals the sum of the squares of the other two sides. 3. **Identify the longest side:** The longest side is 58 yards. 4. **Calculate the squares:** $$40^2 = 1600$$ $$42^2 = 1764$$ $$58^2 = 3364$$ 5. **Check the Pythagorean condition:** $$40^2 + 42^2 = 1600 + 1764 = 3364$$ 6. Since $$3364 = 3364$$, the condition holds true. 7. **Conclusion:** The triangle with sides 40, 42, and 58 yards satisfies the converse of the Pythagorean theorem, so it is a right triangle.