Is the triangle with side lengths of 75 yards, 85 yards, and 40 yards a right triangle?

To determine if a triangle is a right triangle, we can use the Pythagorean theorem, which states that for a triangle with sides (a), (b), and (c) (where (c) is the longest side), the equation (a^2 + b^2 = c^2) must hold true.

In this case, the sides are 75 yards, 85 yards, and 40 yards. Let’s identify the longest side, which is 85 yards.

Now, let’s apply the theorem:

– (a = 75) yards

– (b = 40) yards

– (c = 85) yards

Now we calculate:

1. (a^2 + b^2 = 75^2 + 40^2 = 5625 + 1600 = 7225)
2. (c^2 = 85^2 = 7225)

Since (a^2 + b^2 = c^2) (7225 = 7225), this means the triangle is indeed a right triangle.

Answer: yes