Right triangles and Trig unit test.
1. A triangle has a side length of 24 in. 32 in. and 40 in. Is the triangle acute obtuse or right?
PLZ HELP ASAP
This is a right triangle.
I also use Connexus.
To determine whether the given triangle is acute, obtuse, or right, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's calculate the squares of the given side lengths:
Side length 1: 24^2 = 576
Side length 2: 32^2 = 1024
Side length 3 (the longest side or hypotenuse): 40^2 = 1600
Now, let's check if the sum of the squares of the two shorter sides is equal to the square of the hypotenuse:
576 + 1024 = 1600
Since the sum of the squares of the two shorter sides is equal to the square of the longest side, this triangle is a right triangle.
Therefore, the triangle with side lengths 24 in., 32 in., and 40 in. is a right triangle.
To determine whether the triangle is acute, obtuse, or right, we can use the Pythagorean theorem. According to the theorem, if the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side, then the triangle is right-angled.
In this case, we have side lengths of 24 in, 32 in, and 40 in. To check if it is a right triangle, we can calculate:
24^2 + 32^2 = 576 + 1024 = 1600
(40)^2 = 1600
Since the sum of the squares of the two shorter sides is equal to the square of the longest side (1600 = 1600), the triangle is a right triangle.
Therefore, the triangle with side lengths 24 in, 32 in, and 40 in is a right triangle.