Question

The sides of a triangle are 33, 36, and 18. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.

Answer 1

acute

Explanation:

If the triangle is a right triangle, the lengths of its sides will make the Pythagorean theorem equation true.

If the triangle is a right triangle, then the legs would have to be 18 and 33 since the hypotenuse is always the longest side of a right triangle.

We test the Pythagorean theorem equation with 18 and 33 as legs, a and b, and 36 as the hypotenuse, c.

a² + b² = c²

18² + 33² = 36²

324 + 1089 = 1296

1413 = 1296

Since 1413 = 1296 is a false statement, the triangle is not a right triangle.

To be a right triangle, the square of the hypotenuse would have to be 1413.

Since the square of the hypotenuse is 1296, which is less than 1413, the triangle is acute.

Answer: acute