If a triangle has sides measuring 60, 75, and 45, is it a right triangle?(1 point)
Responses Yes, because 5,625 equals 5,625. Yes, because 5,625 equals 5,625. No, because 5,625 does not equal 3,600. No, because 5,625 does not equal 3,600. No, because 9,225 does not equal 2,025. No, because 9,225 does not equal 2,025. Yes, because 3,600 equals 3,600.
To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem. According to the theorem, 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.
Let's use this theorem to find the length of the hypotenuse in a triangle with sides of length 12 and 16.
Using the Pythagorean theorem:
Hypotenuse^2 = 12^2 + 16^2
Hypotenuse^2 = 144 + 256
Hypotenuse^2 = 400
To find the length of the hypotenuse, we need to take the square root of both sides:
Hypotenuse = √400 = 20
Therefore, the length of the hypotenuse in a triangle with sides of length 12 and 16 is 20 units.
We can use the Pythagorean theorem to find the length of the other leg of the right triangle.
According to the theorem, 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 legs.
Let's use this theorem to find the length of the other leg in the right triangle with a leg of length 12 and a hypotenuse of 16.
Using the Pythagorean theorem:
16^2 = 12^2 + Leg^2
256 = 144 + Leg^2
Leg^2 = 256 - 144
Leg^2 = 112
To find the length of the other leg, we need to take the square root of both sides:
Leg = √112 ≈ 10.6
Therefore, the length of the other leg in the right triangle is approximately 10.6 units.
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 a triangle is a right triangle, we can use the Pythagorean theorem. According to the theorem, 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.
Let's check if this is the case for triangle DEF with sides measuring 50, 40, and 32.
Using the Pythagorean theorem:
(50)^2 = (40)^2 + (32)^2
2500 = 1600 + 1024
2500 = 2624
Since the equation is not true, 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?
If a right triangle has a leg with length 12 and the hypotenuse is 16, how long is the other leg? Round to the nearest tenth, if necessary.
A shortstop is standing in the base path between second and third base when she fields the ball. She is 30 feet from second base and needs to make the throw to first base. Assuming the field is square, how far does she need to throw the ball? Round your answer to the nearest tenth.
Since the field is square, the distance from second base to first base is the same as the distance from home plate to first base. This distance is commonly known as the basepath distance.
To find the basepath distance, we can use the Pythagorean theorem.
Let's consider the shortstop, second base, and first base as the three vertices of a right triangle.
The side adjacent to the right angle is the basepath distance (the distance from second base to first base), and the other two sides are the distances from the shortstop to each base.
Using the Pythagorean theorem:
Basepath distance^2 = distance from second base^2 + distance from shortstop^2
Basepath distance^2 = 30^2 + 90^2
Basepath distance^2 = 900 + 8100
Basepath distance^2 = 9000
To find the basepath distance, we need to take the square root of both sides:
Basepath distance = √9000 ≈ 94.9
Therefore, the shortstop needs to throw the ball approximately 94.9 feet to reach first base.