A triangle has sides with lengths of 42 miles, 58 miles, and 40 miles. Is it a right triangle?

To determine if a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Step 1: Identify the longest side. In this case, the longest side is 58 miles.

Step 2: Square the lengths of all sides: 42^2 = 1764 58^2 = 3364 40^2 = 1600

Step 3: Check if the square of the longest side is equal to the sum of the squares of the other two sides: 3364 = 1764 + 1600 3364 = 3364

Since the equation is true, the triangle is a right triangle.