does 60, 75, and 45 make a right triangle?
To determine if a triangle is a right triangle, we can apply 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.
In this case, we have side lengths of 60, 75, and 45. Let's calculate the squares of these side lengths:
60² = 3600
75² = 5625
45² = 2025
Now, let's check if these values satisfy the Pythagorean theorem.
The largest side length is 75, so this will be the potential hypotenuse. We can pair the other two side lengths as the other sides of the triangle:
3600 + 2025 = 5625
Since the sum of the squares of the two smaller side lengths is equal to the square of the largest side length (5625 = 5625), the triangle with side lengths 60, 75, and 45 is a right triangle.