A triangle has sides with lengths of 30 feet, 77 feet, and 78 feet. 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. This is often written as a^2 + b^2 = c^2.

In this case, the three sides are 30 feet, 77 feet, and 78 feet. If this is a right triangle, the 78 feet side should be the hypotenuse, as it is the longest side.

So, we can plug these values into the Pythagorean theorem:

(30)^2 + (77)^2 = (78)^2 900 + 5929 = 6084

The left side of the equation equals 6829, and the right side equals 6084. Since these values are not equal, this triangle is not a right triangle.