Since a triangle has a total of 180°, and one angle in the right triangle is 90°, the sum of the other two angles must be 180° - 90° = 90°.
Therefore, the third angle in the right triangle is 90° - 50° = 40°.
If a right triangle has an angle that is 50°, what is the third angle in the triangle?
29 answers
In the picture, one angle is labeled 135°., and the two lines are parallel. Which other three angles will be 135°
If two lines are parallel and a transversal intersects them, the alternate interior angles are congruent.
In this case, if one angle is labeled 135°, then the other three angles that will be 135° are:
1. The corresponding angle on the other side of the transversal.
2. The vertical angle to the angle labeled 135°.
3. The alternate interior angle to the angle labeled 135°.
In this case, if one angle is labeled 135°, then the other three angles that will be 135° are:
1. The corresponding angle on the other side of the transversal.
2. The vertical angle to the angle labeled 135°.
3. The alternate interior angle to the angle labeled 135°.
If a triangle has sides measuring 15, 25, and 20, is it a right triangle?
To determine if a triangle is a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, 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 (the hypotenuse).
Let's check if the triangle with sides measuring 15, 25, and 20 satisfies this condition:
The longest side is 25.
The sum of the squares of the two shorter sides is: 15^2 + 20^2 = 225 + 400 = 625.
The square of the length of the longest side is: 25^2 = 625.
Since the sum of the squares of the two shorter sides is equal to the square of the length of the longest side (625 = 625), the triangle with sides 15, 25, and 20 satisfies the Pythagorean theorem.
Therefore, the triangle is a right triangle.
Let's check if the triangle with sides measuring 15, 25, and 20 satisfies this condition:
The longest side is 25.
The sum of the squares of the two shorter sides is: 15^2 + 20^2 = 225 + 400 = 625.
The square of the length of the longest side is: 25^2 = 625.
Since the sum of the squares of the two shorter sides is equal to the square of the length of the longest side (625 = 625), the triangle with sides 15, 25, and 20 satisfies the Pythagorean theorem.
Therefore, the triangle is a right triangle.
so what is the answer?
The answer is that the triangle with sides measuring 15, 25, and 20 is a right triangle.
If a triangle has sides measuring 15, 25, and 20, is it a right triangle?(1 point)
Responses
Yes, because 625 equals 625.
Yes, because 625 equals 625.
No, because 850 doesn't equal 400.
No, because 850 doesn't equal 400.
Yes, because 850 equals 850.
Yes, because 850 equals 850.
No, because 1,025 doesn't equal 225.
Responses
Yes, because 625 equals 625.
Yes, because 625 equals 625.
No, because 850 doesn't equal 400.
No, because 850 doesn't equal 400.
Yes, because 850 equals 850.
Yes, because 850 equals 850.
No, because 1,025 doesn't equal 225.
The correct answer is:
No, because 850 doesn't equal 400.
No, because 850 doesn't equal 400.
If triangle ABC has sides measuring 21, 28, and 35, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it isn't a right triangle, answer with the number 0.
To determine if a triangle is a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, 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 (the hypotenuse).
Let's check if the triangle with sides measuring 21, 28, and 35 satisfies this condition:
The longest side is 35.
The sum of the squares of the two shorter sides is: 21^2 + 28^2 = 441 + 784 = 1225.
The square of the length of the longest side is: 35^2 = 1225.
Since the sum of the squares of the two shorter sides is equal to the square of the length of the longest side (1225 = 1225), the triangle with sides 21, 28, and 35 satisfies the Pythagorean theorem.
Therefore, the triangle is a right triangle. The answer is 90.
Let's check if the triangle with sides measuring 21, 28, and 35 satisfies this condition:
The longest side is 35.
The sum of the squares of the two shorter sides is: 21^2 + 28^2 = 441 + 784 = 1225.
The square of the length of the longest side is: 35^2 = 1225.
Since the sum of the squares of the two shorter sides is equal to the square of the length of the longest side (1225 = 1225), the triangle with sides 21, 28, and 35 satisfies the Pythagorean theorem.
Therefore, the triangle is a right triangle. The answer is 90.
If a triangle has sides of length 30 and 40, how long is the hypotenuse?
To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem, which 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.
Let's denote the lengths of the two shorter sides as a = 30 and b = 40.
The Pythagorean theorem can be written as:
c^2 = a^2 + b^2,
where c represents the length of the hypotenuse.
By substituting the given side lengths, we have:
c^2 = 30^2 + 40^2 = 900 + 1600 = 2500.
Taking the square root of both sides gives us:
c = sqrt(2500) = 50.
Thus, the length of the hypotenuse is 50.
Let's denote the lengths of the two shorter sides as a = 30 and b = 40.
The Pythagorean theorem can be written as:
c^2 = a^2 + b^2,
where c represents the length of the hypotenuse.
By substituting the given side lengths, we have:
c^2 = 30^2 + 40^2 = 900 + 1600 = 2500.
Taking the square root of both sides gives us:
c = sqrt(2500) = 50.
Thus, the length of the hypotenuse is 50.
If a right triangle has a leg length 7.5 and the hypotenuse if 12.5, how long is the other leg?
To find the length of the other leg in a right triangle, we can use the Pythagorean theorem, which 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.
Let's denote the length of one leg as a = 7.5, and the length of the hypotenuse as c = 12.5.
The Pythagorean theorem can be written as:
c^2 = a^2 + b^2,
where b represents the length of the other leg.
By substituting the given side lengths, we have:
12.5^2 = 7.5^2 + b^2,
156.25 = 56.25 + b^2.
Subtracting 56.25 from both sides:
100 = b^2.
Taking the square root of both sides:
b = sqrt(100) = 10.
Thus, the length of the other leg is 10.
Let's denote the length of one leg as a = 7.5, and the length of the hypotenuse as c = 12.5.
The Pythagorean theorem can be written as:
c^2 = a^2 + b^2,
where b represents the length of the other leg.
By substituting the given side lengths, we have:
12.5^2 = 7.5^2 + b^2,
156.25 = 56.25 + b^2.
Subtracting 56.25 from both sides:
100 = b^2.
Taking the square root of both sides:
b = sqrt(100) = 10.
Thus, the length of the other leg is 10.
Sarah is standing at the red X. She wants to go to the library and has decided to cut across the edge of the park to get there. If she is 2 miles down Elm Street, and the Library is 3 miles down Oak Street, how far will she have to walk to get to the library? Round to the nearest tenth.
To find the distance Sarah will have to walk to get to the library, we can use the Pythagorean theorem since Sarah is cutting across the edge of the park.
Let's consider Elm Street as the horizontal leg of a right triangle and Oak Street as the vertical leg. The distance she needs to walk is the hypotenuse of the right triangle formed.
Using the given information, with Elm Street being 2 miles and Oak Street being 3 miles, we can calculate the distance she needs to walk using the Pythagorean theorem:
Distance^2 = (2 miles)^2 + (3 miles)^2
Distance^2 = 4 + 9
Distance^2 = 13
Taking the square root of both sides:
Distance ≈ √13 ≈ 3.61 miles (rounded to the nearest tenth)
Therefore, Sarah will have to walk approximately 3.61 miles to get to the library.
Let's consider Elm Street as the horizontal leg of a right triangle and Oak Street as the vertical leg. The distance she needs to walk is the hypotenuse of the right triangle formed.
Using the given information, with Elm Street being 2 miles and Oak Street being 3 miles, we can calculate the distance she needs to walk using the Pythagorean theorem:
Distance^2 = (2 miles)^2 + (3 miles)^2
Distance^2 = 4 + 9
Distance^2 = 13
Taking the square root of both sides:
Distance ≈ √13 ≈ 3.61 miles (rounded to the nearest tenth)
Therefore, Sarah will have to walk approximately 3.61 miles to get to the library.
Use the Pythagorean Theorem to find the distance between the two points (1,2) and (5,7). Round to the nearest tenth
To find the distance between two points (x1, y1) and (x2, y2) on a coordinate plane, we can use the distance formula or apply the Pythagorean theorem to the corresponding right triangle.
Let's find the distance between the points (1, 2) and (5, 7):
Horizontal difference (Δx) = x2 - x1 = 5 - 1 = 4
Vertical difference (Δy) = y2 - y1 = 7 - 2 = 5
Using these differences, we can find the distance (d) using the Pythagorean theorem:
d^2 = (Δx)^2 + (Δy)^2
d^2 = 4^2 + 5^2
d^2 = 16 + 25
d^2 = 41
Taking the square root of both sides:
d ≈ √41 ≈ 6.4 (rounded to the nearest tenth)
Therefore, the distance between the points (1, 2) and (5, 7) is approximately 6.4 units.
Let's find the distance between the points (1, 2) and (5, 7):
Horizontal difference (Δx) = x2 - x1 = 5 - 1 = 4
Vertical difference (Δy) = y2 - y1 = 7 - 2 = 5
Using these differences, we can find the distance (d) using the Pythagorean theorem:
d^2 = (Δx)^2 + (Δy)^2
d^2 = 4^2 + 5^2
d^2 = 16 + 25
d^2 = 41
Taking the square root of both sides:
d ≈ √41 ≈ 6.4 (rounded to the nearest tenth)
Therefore, the distance between the points (1, 2) and (5, 7) is approximately 6.4 units.
Find the length of the interior diagonal if a rectangular prism has a width of 6 inches, a length of 8 inches and a height of 10 inches. Round to the nearest tenth.
To find the length of the interior diagonal of a rectangular prism, we can use the Pythagorean theorem. The interior diagonal is the line segment connecting opposite vertices inside the rectangular prism.
Let's denote the width of the rectangular prism as a = 6 inches, the length as b = 8 inches, and the height as c = 10 inches.
Applying the Pythagorean theorem, the length of the interior diagonal (d) can be found using the formula:
d^2 = a^2 + b^2 + c^2
Substituting the given values, we have:
d^2 = 6^2 + 8^2 + 10^2
d^2 = 36 + 64 + 100
d^2 = 200
Taking the square root of both sides:
d ≈ √200 ≈ 14.1 (rounded to the nearest tenth)
Therefore, the length of the interior diagonal of the rectangular prism is approximately 14.1 inches.
Let's denote the width of the rectangular prism as a = 6 inches, the length as b = 8 inches, and the height as c = 10 inches.
Applying the Pythagorean theorem, the length of the interior diagonal (d) can be found using the formula:
d^2 = a^2 + b^2 + c^2
Substituting the given values, we have:
d^2 = 6^2 + 8^2 + 10^2
d^2 = 36 + 64 + 100
d^2 = 200
Taking the square root of both sides:
d ≈ √200 ≈ 14.1 (rounded to the nearest tenth)
Therefore, the length of the interior diagonal of the rectangular prism is approximately 14.1 inches.
If another pyramid were built in Egypt that had a square base measuring 2,640 feet and had a slant height of 5,903 feet, how tall would the pyramid be? Round to the nearest whole foot.(1 point)
To find the height of the pyramid, we can use the Pythagorean theorem. The slant height of the pyramid represents the hypotenuse of a right triangle, with the height being one of the legs and half the length of the base being the other leg.
Let's denote the height of the pyramid as h, the slant height as s, and the length of the base as b.
Applying the Pythagorean theorem, we have:
s^2 = h^2 + (b/2)^2
Substituting the given values, we have:
(5903 feet)^2 = h^2 + (2640 feet/2)^2
34858009 feet^2 = h^2 + 3481600 feet^2
Now, we can solve for h:
h^2 = 34858009 feet^2 - 3481600 feet^2
h^2 = 31376409 feet^2
Taking the square root of both sides:
h ≈ 5598 feet (rounded to the nearest whole foot)
Therefore, the height of the pyramid would be approximately 5598 feet.
Let's denote the height of the pyramid as h, the slant height as s, and the length of the base as b.
Applying the Pythagorean theorem, we have:
s^2 = h^2 + (b/2)^2
Substituting the given values, we have:
(5903 feet)^2 = h^2 + (2640 feet/2)^2
34858009 feet^2 = h^2 + 3481600 feet^2
Now, we can solve for h:
h^2 = 34858009 feet^2 - 3481600 feet^2
h^2 = 31376409 feet^2
Taking the square root of both sides:
h ≈ 5598 feet (rounded to the nearest whole foot)
Therefore, the height of the pyramid would be approximately 5598 feet.
In making a rectangular barn door, Gena wanted to add an X on the front of the door, following the diagonals of the rectangular door, as shown in the picture. If the door measures 4 feet wide and is 6 feet tall, how long does she need to cut the boards to make each piece of the X? Round to the nearest hundredth
To find the length of each board needed to make the X on the front of the rectangular door, we can use the Pythagorean theorem. The length of each board represents the hypotenuse of a right triangle, with the width and height of the door being the other two sides.
Let's denote the length of each board needed as l, the width of the door as w, and the height of the door as h.
Applying the Pythagorean theorem, we have:
l^2 = w^2 + h^2
Substituting the given values, we have:
l^2 = 4^2 + 6^2
l^2 = 16 + 36
l^2 = 52
Taking the square root of both sides:
l ≈ √52 ≈ 7.21 (rounded to the nearest hundredth)
Therefore, Gena needs to cut each board to a length of approximately 7.21 feet to make each piece of the X.
Let's denote the length of each board needed as l, the width of the door as w, and the height of the door as h.
Applying the Pythagorean theorem, we have:
l^2 = w^2 + h^2
Substituting the given values, we have:
l^2 = 4^2 + 6^2
l^2 = 16 + 36
l^2 = 52
Taking the square root of both sides:
l ≈ √52 ≈ 7.21 (rounded to the nearest hundredth)
Therefore, Gena needs to cut each board to a length of approximately 7.21 feet to make each piece of the X.
Explain when you can use the Pythagorean Theorem, and why/when you would use the Converse of the Pythagorean Theorem.
The Pythagorean theorem can be used when we have a right triangle, which is a triangle that has one angle measuring 90 degrees. It 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.
We can use the Pythagorean theorem in a right triangle to calculate the length of any side (including the hypotenuse) if we know the lengths of the other two sides.
On the other hand, the Converse of the Pythagorean theorem can be used when we have three side lengths and want to determine if these lengths form a right triangle. The Converse states that if the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
So, we would use the Converse of the Pythagorean theorem when given three side lengths of a triangle and we need to determine if the triangle is a right triangle or not.
In summary:
- We use the Pythagorean theorem to calculate a missing side length (including the hypotenuse) in a right triangle when given the lengths of the other two sides.
- We use the Converse of the Pythagorean theorem to determine if a triangle is a right triangle or not when given three side lengths.
We can use the Pythagorean theorem in a right triangle to calculate the length of any side (including the hypotenuse) if we know the lengths of the other two sides.
On the other hand, the Converse of the Pythagorean theorem can be used when we have three side lengths and want to determine if these lengths form a right triangle. The Converse states that if the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
So, we would use the Converse of the Pythagorean theorem when given three side lengths of a triangle and we need to determine if the triangle is a right triangle or not.
In summary:
- We use the Pythagorean theorem to calculate a missing side length (including the hypotenuse) in a right triangle when given the lengths of the other two sides.
- We use the Converse of the Pythagorean theorem to determine if a triangle is a right triangle or not when given three side lengths.
Find the slant height of the square pyramid. Round to the nearest hundredth. 5 up the middle
3 on the bottum
3 on the bottum
To find the slant height of a square pyramid, we need to know the height of the pyramid and the length of one side of the base. However, in the provided information, only the lengths of the sides are given. The height of the pyramid is not specified.
Therefore, without the height of the pyramid, we cannot determine the slant height. The slant height depends on both the height of the pyramid and the length of one side of the base.
If the height is provided, we can proceed to calculate the slant height using the Pythagorean theorem, as it forms a right triangle with the height, slant height, and half the length of the base.
Therefore, without the height of the pyramid, we cannot determine the slant height. The slant height depends on both the height of the pyramid and the length of one side of the base.
If the height is provided, we can proceed to calculate the slant height using the Pythagorean theorem, as it forms a right triangle with the height, slant height, and half the length of the base.
1 answer