What is the relationship of the sides in this triangle based on the Pythagorean Theorem? (1 point)
m^2 + n^2 =
c^2
If a triangle has sides measuring 60, 75, and 45, is it a right triangle?
A. Yes, because 5,625 equals 5,625
B. No, because 9,225 does not equal 2,025
C. No, because 5,625 does not equal 3,600
D. Yes, because 3,600 equals 3,600
C. No, because 5,625 does not equal 3,600
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 0.
To determine if the triangle is a right triangle, we can check if the square of the longest side is equal to the sum of the squares of the other two sides.
Sum of squares of shorter sides: 40^2 + 32^2 = 1600 + 1024 = 2624
Square of longest side: 50^2 = 2500
Since 2624 is not equal to 2500, the triangle DEF is not a right triangle. Therefore, the answer is 0.
If a triangle has sides of length 12 and 16, how long is the hypotenuse?
To find the length of the hypotenuse, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
So, in this case:
Length of one side = 12
Length of another side = 16
Let's assume the length of the hypotenuse is 'c'.
Using the Pythagorean theorem:
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
To find the length of the hypotenuse, we need to take the square root of both sides:
c = √400
c = 20
Therefore, the hypotenuse has a length of 20.
If a right triangle has a leg with a length of 12 and the hypotenuse is 16, how long is the other leg? Round to the nearest tenth, if necessary
To find the length of the other leg in 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 is equal to the sum of the squares of the lengths of the other two sides.
So, in this case:
Length of one leg = 12
Length of the hypotenuse = 16
Let's assume the length of the other leg is 'x'.
Using the Pythagorean theorem:
16^2 = 12^2 + x^2
256 = 144 + x^2
x^2 = 256 - 144
x^2 = 112
To find the length of the other leg, we need to take the square root of both sides:
x = √112
x ≈ 10.60 (rounded to the nearest tenth)
Therefore, the other leg has a length of approximately 10.60.