If triangle DEF has sides measuring 50, 40, and 32 is the triangle a right triangle if it is a right triangle answer with the number 90 if it is not a right triangle answer with the number zero
To determine whether triangle DEF is a right triangle, we can use the Pythagorean theorem.
The Pythagorean theorem 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.
If triangle DEF is a right triangle, then we should have:
(Length of the hypotenuse)^2 = (Length of one side)^2 + (Length of the other side)^2
Let's check this condition using the given side lengths of triangle DEF:
(Length of the hypotenuse)^2 = 50^2 = 2500
(Length of one side)^2 + (Length of the other side)^2 = 40^2 + 32^2 = 1600 + 1024 = 2624
Since the two values do not match, we can conclude that triangle DEF is not a right triangle.
Therefore, the triangle DEF is not a right triangle, and the answer is zero.
To determine if the triangle DEF is a right triangle, we can make use of the Pythagorean theorem. According to the Pythagorean theorem, in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Let's calculate the squares of the three sides of triangle DEF:
- Side DE: 50^2 = 2500
- Side EF: 40^2 = 1600
- Side FD: 32^2 = 1024
Now, let's check if the sum of the squares of the shorter two sides (EF and FD) is equal to the square of the longest side (DE):
1600 + 1024 = 2624
Since 2624 is not equal to 2500, triangle DEF is not a right triangle.
The triangle DEF is not a right triangle, so the answer is 0.
To determine if a triangle is a right triangle, you can use the Pythagorean theorem. The Pythagorean theorem 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 other two sides.
To apply the Pythagorean theorem, you need to square the lengths of the sides of the triangle and check if the resulting sum is equal to the square of the longest side (the hypotenuse). Let's calculate it for the given triangle DEF:
Side DE = 50
Side EF = 40
Side FD = 32
Now let's find the squares of these lengths:
DE^2 = 50^2 = 2500
EF^2 = 40^2 = 1600
FD^2 = 32^2 = 1024
To determine if triangle DEF is a right triangle, we need to check if the sum of the squares of the two shorter sides (DE^2 + EF^2) is equal to the square of the longest side (FD^2).
DE^2 + EF^2 = 2500 + 1600 = 4100
FD^2 = 1024
Since DE^2 + EF^2 (4100) is not equal to FD^2 (1024), triangle DEF is not a right triangle. Therefore, the answer is zero.