A triangle has sides that measure 3 feet, 4 feet, and 5 feet. Will it be acute, obtuse, or right?
gotta show how I got my answer.
Thank you guys!
To determine whether a triangle is acute, obtuse, or right, we need to examine the angles formed by its sides.
In a right triangle, one angle measures exactly 90 degrees. This occurs when the sum of the squares of the two shorter sides equals the square of the longest side. In this case, the triangle has side lengths of 3 feet, 4 feet, and 5 feet. Let's check if it satisfies the Pythagorean theorem.
Using the theorem: (3^2) + (4^2) = 9 + 16 = 25
Therefore, the sum of the squares of the two shorter sides equals the square of the longest side. Since 25 is the square of 5, we can conclude that the triangle with side lengths 3 feet, 4 feet, and 5 feet is a right triangle.
So, to answer your question, the triangle in question is right.
Remember, for any triangle, you can use the Pythagorean theorem to determine whether it is right.
by now you should be able to recognize the most basic 3-4-5 right triangle!
Recall the Pythagorean Theorem.