To determine whether 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 other two sides.
Let's denote the sides of the triangle as follows:
a = 21 miles
b = 28 miles
c = 35 miles
If the triangle is a right triangle, then it should satisfy the equation a^2 + b^2 = c^2.
Substituting the values, we have:
21^2 + 28^2 = 35^2
441 + 784 = 1225
1225 = 1225
Since the equation holds true, we can conclude that the triangle with side lengths of 21 miles, 28 miles, and 35 miles is indeed a right triangle.