The sum of all angles in a triangle is 180°.
We know that one angle is 90° (as it is a right triangle) and another angle is 65°.
To find the third angle, we can subtract the sum of the two given angles from 180°:
180° - 90° - 65° = 25°
Therefore, the third angle in the triangle is 25°.
If a right triangle has an angle that is 65° , what is the third angle in the triangle?(1 point)
38 answers
A rightward inclined transversal passes through two horizontal parallel lines labeled upper S and upper T. Angles formed at the intersection point of line upper S are labeled clockwise from the top: 1, 2, 4, and 3. Corresponding angles formed at the intersection point of line upper N are labeled clockwise from the top: 5, 22 degrees, 7, and 6.
In the picture, one angle is labeled 22° and lines S and T are parallel. Which other three angles will be 22° ? Separate each angle number with a comma.
(1 point)
In the picture, one angle is labeled 22° and lines S and T are parallel. Which other three angles will be 22° ? Separate each angle number with a comma.
(1 point)
In a rightward inclined transversal passing through two parallel lines, the corresponding angles are equal.
Given that angle 5 is labeled as 22°, this means that angle 1, angle 3, and angle 7 will also be 22°.
Therefore, the other three angles that will be 22° are 1, 3, and 7.
Given that angle 5 is labeled as 22°, this means that angle 1, angle 3, and angle 7 will also be 22°.
Therefore, the other three angles that will be 22° are 1, 3, and 7.
bot, that is wrong
Apologies for the incorrect response. Let's reconsider the angles:
In a rightward inclined transversal, angle 1 and angle 5 are corresponding angles. If angle 5 is labeled as 22°, then angle 1 will also be 22°.
Therefore, the other three angles that will be 22° are angles 1, 5, and their corresponding angle on the other side.
In a rightward inclined transversal, angle 1 and angle 5 are corresponding angles. If angle 5 is labeled as 22°, then angle 1 will also be 22°.
Therefore, the other three angles that will be 22° are angles 1, 5, and their corresponding angle on the other side.
No bot, the answers are actually 2, 3, and 6
Apologies for the confusion and incorrect response earlier. You are correct.
In a rightward inclined transversal passing through two parallel lines, the corresponding angles on different sides of the transversal are equal.
Given that angle 5 is labeled as 22°, this means that angle 6, angle 2, and angle 3 will also be 22°.
Therefore, the other three angles that will be 22° are 2, 3, and 6. Thank you for pointing out the error.
In a rightward inclined transversal passing through two parallel lines, the corresponding angles on different sides of the transversal are equal.
Given that angle 5 is labeled as 22°, this means that angle 6, angle 2, and angle 3 will also be 22°.
Therefore, the other three angles that will be 22° are 2, 3, and 6. Thank you for pointing out the error.
Use the image to answer the question.
A triangle has the vertices labeled upper M upper N upper O. Upper N upper O is labeled m, upper M upper N is labeled o, and upper O upper M is labeled n. Angle upper N measures 62 degrees and angle upper M measures 28 degrees.
What is the relationship of the sides in this triangle based on the Pythagorean Theorem?
(1 point)
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A triangle has the vertices labeled upper M upper N upper O. Upper N upper O is labeled m, upper M upper N is labeled o, and upper O upper M is labeled n. Angle upper N measures 62 degrees and angle upper M measures 28 degrees.
What is the relationship of the sides in this triangle based on the Pythagorean Theorem?
(1 point)
$$
Skip to navigation
Without the provided image, it is not possible to determine the relationship of the sides in the triangle based on 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. However, without information about the lengths or specific angles of the triangle, it is not possible to apply the Pythagorean Theorem in this case.
Use equation m²+n²=
I apologize, but I still need more information or the image to provide a complete answer. The equation you provided, m² + n² = ?, cannot be solved without further context or values for either m or n. Could you please provide more information or the missing value in the equation?
Use the image to answer the question.
A triangle has the vertices labeled upper M upper N upper O. Upper N upper O is labeled m, upper M upper N is labeled o, and upper O upper M is labeled n. Angle upper N measures 62 degrees and angle upper M measures 28 degrees.
What is the relationship of the sides in this triangle based on the Pythagorean Theorem?
(1 point)
m²+n²=
A triangle has the vertices labeled upper M upper N upper O. Upper N upper O is labeled m, upper M upper N is labeled o, and upper O upper M is labeled n. Angle upper N measures 62 degrees and angle upper M measures 28 degrees.
What is the relationship of the sides in this triangle based on the Pythagorean Theorem?
(1 point)
m²+n²=
I apologize for any confusion, but unfortunately, I cannot see or access the provided image. Without the image or specific length measurements of the sides, it is not possible to determine the relationship of the sides in the triangle using the Pythagorean Theorem. The Pythagorean Theorem can only be applied in a right triangle, where the squares of the lengths of the two shorter sides (legs) are equal to the square of the length of the longest side (hypotenuse). If you can provide additional information or the missing value, I would be happy to assist you further.
If a triangle has sides measuring 60, 75, and 45, is it a right triangle?(1 point)
Responses
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.
Yes, because 3,600 equals 3,600.
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.
Responses
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.
Yes, because 3,600 equals 3,600.
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.
To determine if a triangle is a right triangle, we need to check if it satisfies the Pythagorean Theorem. According to the Pythagorean Theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the sides measure 60, 75, and 45. Let's check if it is a right triangle:
60^2 + 45^2 = 3600 + 2025 = 5625
75^2 = 5625
Based on the calculations, 5625 equals 5625. Therefore, the triangle satisfies the Pythagorean Theorem, indicating that it is a right triangle.
Hence, the correct answer is:
Yes, because 5,625 equals 5,625.
In this case, the sides measure 60, 75, and 45. Let's check if it is a right triangle:
60^2 + 45^2 = 3600 + 2025 = 5625
75^2 = 5625
Based on the calculations, 5625 equals 5625. Therefore, the triangle satisfies the Pythagorean Theorem, indicating that it is a right triangle.
Hence, the correct answer is:
Yes, because 5,625 equals 5,625.
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.(1 point)
To determine if a triangle is a right triangle, we need to check if it satisfies the Pythagorean Theorem. According to the Pythagorean Theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the sides of triangle DEF measure 50, 40, and 32. Let's check if it is a right triangle:
If 40 and 32 are the lengths of the two smaller sides, then according to the Pythagorean Theorem, the square of the hypotenuse (50) should be equal to the sum of the squares of the other two sides:
40^2 + 32^2 = 1600 + 1024 = 2624
50^2 = 2500
Since 2624 is not equal to 2500, the triangle DEF does not satisfy the Pythagorean Theorem. Therefore, the triangle is not a right triangle.
Hence, the correct answer is:
0
In this case, the sides of triangle DEF measure 50, 40, and 32. Let's check if it is a right triangle:
If 40 and 32 are the lengths of the two smaller sides, then according to the Pythagorean Theorem, the square of the hypotenuse (50) should be equal to the sum of the squares of the other two sides:
40^2 + 32^2 = 1600 + 1024 = 2624
50^2 = 2500
Since 2624 is not equal to 2500, the triangle DEF does not satisfy the Pythagorean Theorem. Therefore, the triangle is not a right triangle.
Hence, the correct answer is:
0
If a triangle has sides of length 12 and 16, how long is the hypotenuse?(1 point)
To find the length of the hypotenuse in 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 is equal to the sum of the squares of the lengths of the other two sides.
In this case, the given sides have lengths of 12 and 16. Let's calculate the length of the hypotenuse:
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 is 20.
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.
In this case, the given sides have lengths of 12 and 16. Let's calculate the length of the hypotenuse:
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 is 20.
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.(1 point)
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 two legs.
In this case, one leg has a length of 12, and the hypotenuse has a length of 16. Let's calculate the length of the other leg:
Let the length of the other leg be x.
Using the Pythagorean Theorem:
x² + 12² = 16²
x² + 144 = 256
x² = 256 - 144
x² = 112
x ≈ √112
x ≈ 10.6
Therefore, the length of the other leg is approximately 10.6 when rounded to the nearest tenth.
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 two legs.
In this case, one leg has a length of 12, and the hypotenuse has a length of 16. Let's calculate the length of the other leg:
Let the length of the other leg be x.
Using the Pythagorean Theorem:
x² + 12² = 16²
x² + 144 = 256
x² = 256 - 144
x² = 112
x ≈ √112
x ≈ 10.6
Therefore, the length of the other leg is approximately 10.6 when rounded to the nearest tenth.
Use the image to answer the question.
An illustration shows a square with smaller squares representing baseball plates on the top left, top right, and bottom right vertices. The bottom left vertex has a pentagon that represents home plate. A stick figure is located on the top of the square and the measurement from the right vertex to the stick figure is labeled 30 feet. A dashed diagonal line runs from the stick figure to the inner right side of the square, forming the hypotenuse of a triangle. The top right side of the square forms the right angle of the triangle and is marked with a right angle symbol. The outer right side of the square is labeled 90 feet.
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.
(1 point)
An illustration shows a square with smaller squares representing baseball plates on the top left, top right, and bottom right vertices. The bottom left vertex has a pentagon that represents home plate. A stick figure is located on the top of the square and the measurement from the right vertex to the stick figure is labeled 30 feet. A dashed diagonal line runs from the stick figure to the inner right side of the square, forming the hypotenuse of a triangle. The top right side of the square forms the right angle of the triangle and is marked with a right angle symbol. The outer right side of the square is labeled 90 feet.
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.
(1 point)
Based on the given description, we can determine that this is a right triangle with the right angle at the top right corner of the square. The right side of the square (adjacent to the right angle) is labeled as 90 feet, and the stick figure is 30 feet away from the right vertex of the square.
To find the distance she needs to throw the ball, we need to calculate the length of the hypotenuse of the right triangle.
Using the Pythagorean Theorem:
hypotenuse² = 30² + 90²
hypotenuse² = 900 + 8100
hypotenuse² = 9000
To find the length of the hypotenuse, we need to take the square root of both sides:
hypotenuse ≈ √9000 ≈ 94.868
Therefore, she needs to throw the ball a distance of approximately 94.9 feet when rounded to the nearest tenth.
To find the distance she needs to throw the ball, we need to calculate the length of the hypotenuse of the right triangle.
Using the Pythagorean Theorem:
hypotenuse² = 30² + 90²
hypotenuse² = 900 + 8100
hypotenuse² = 9000
To find the length of the hypotenuse, we need to take the square root of both sides:
hypotenuse ≈ √9000 ≈ 94.868
Therefore, she needs to throw the ball a distance of approximately 94.9 feet when rounded to the nearest tenth.
Use the image to answer the question.
A graph shows quadrant 1 with the x-axis and y-axis ranging from 0 to positive 9. Data points marked are at left parenthesis 3 comma 2 right parenthesis, and left parenthesis 7 comma 8 right parenthesis. A straight line joins the two points forming a positive slope.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.
(1 point)
A graph shows quadrant 1 with the x-axis and y-axis ranging from 0 to positive 9. Data points marked are at left parenthesis 3 comma 2 right parenthesis, and left parenthesis 7 comma 8 right parenthesis. A straight line joins the two points forming a positive slope.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.
(1 point)
To find the length between the two points (3, 2) and (7, 8) using the Pythagorean Theorem, we need to calculate the distance between these two points.
The distance formula is derived from the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Using the distance formula, the length between the two points (x1, y1) and (x2, y2) is given by:
Distance = √((x2 - x1)² + (y2 - y1)²)
In this case, (x1, y1) = (3, 2) and (x2, y2) = (7, 8).
Calculating the distance:
Distance = √((7 - 3)² + (8 - 2)²)
Distance = √(4² + 6²)
Distance = √(16 + 36)
Distance = √52
Rounded to the nearest hundredth, the distance between the two points is approximately 7.21.
Therefore, the length between the points (3, 2) and (7, 8) is approximately 7.21 when rounded to the nearest hundredth.
The distance formula is derived from the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Using the distance formula, the length between the two points (x1, y1) and (x2, y2) is given by:
Distance = √((x2 - x1)² + (y2 - y1)²)
In this case, (x1, y1) = (3, 2) and (x2, y2) = (7, 8).
Calculating the distance:
Distance = √((7 - 3)² + (8 - 2)²)
Distance = √(4² + 6²)
Distance = √(16 + 36)
Distance = √52
Rounded to the nearest hundredth, the distance between the two points is approximately 7.21.
Therefore, the length between the points (3, 2) and (7, 8) is approximately 7.21 when rounded to the nearest hundredth.
Use the image to answer the question.
An illustration shows a square pyramid with labeled parts. The front and left faces of the pyramid and base are visible. The back and right faces are not visible. The back and right base edges are not visible but their position is indicated by a dashed line. The left base edge shows a length of 16 feet. A dotted line extends from the interior of the vertex straight down to the center of the base and shows a height of 15. A right angle is indicated where the dotted height line meets the base.
Find the slant height of the square pyramid.
(1 point)
An illustration shows a square pyramid with labeled parts. The front and left faces of the pyramid and base are visible. The back and right faces are not visible. The back and right base edges are not visible but their position is indicated by a dashed line. The left base edge shows a length of 16 feet. A dotted line extends from the interior of the vertex straight down to the center of the base and shows a height of 15. A right angle is indicated where the dotted height line meets the base.
Find the slant height of the square pyramid.
(1 point)
To find the slant height of the square pyramid, we can use the Pythagorean Theorem.
In the given illustration, we have a right triangle formed by the slant height, the height, and half of the base of the pyramid.
Using the Pythagorean Theorem:
slant height^2 = height^2 + (1/2 * base)^2
slant height^2 = 15^2 + (1/2 * 16)^2
slant height^2 = 225 + 64
slant height^2 = 289
To find the slant height, we need to take the square root of both sides:
slant height ≈ √289 ≈ 17
Therefore, the slant height of the square pyramid is approximately 17 feet.
In the given illustration, we have a right triangle formed by the slant height, the height, and half of the base of the pyramid.
Using the Pythagorean Theorem:
slant height^2 = height^2 + (1/2 * base)^2
slant height^2 = 15^2 + (1/2 * 16)^2
slant height^2 = 225 + 64
slant height^2 = 289
To find the slant height, we need to take the square root of both sides:
slant height ≈ √289 ≈ 17
Therefore, the slant height of the square pyramid is approximately 17 feet.
Bot, one side length of the pyramid is 8 and the other is 15
Apologies for the previous incorrect response. Based on the new information provided, let's recalculate the slant height.
In the given illustration, we have a right triangle formed by the slant height, the height, and one of the sides of the pyramid (not the base).
Using the Pythagorean Theorem:
slant height² = height² + side²
slant height² = 15² + 8²
slant height² = 225 + 64
slant height² = 289
To find the slant height, we need to take the square root:
slant height ≈ √289 ≈ 17
Therefore, the slant height of the square pyramid is approximately 17 units or 17 feet.
In the given illustration, we have a right triangle formed by the slant height, the height, and one of the sides of the pyramid (not the base).
Using the Pythagorean Theorem:
slant height² = height² + side²
slant height² = 15² + 8²
slant height² = 225 + 64
slant height² = 289
To find the slant height, we need to take the square root:
slant height ≈ √289 ≈ 17
Therefore, the slant height of the square pyramid is approximately 17 units or 17 feet.
what is the square root of 241
The square root of 241 is approximately 15.524.
Use the image to answer the question.
An illustration of a rectangular prism is shown with labeled parts. The top, front and right sides are visible. The bottom, left, and rear sides are not visible, but their positions are indicated by dashed lines. The vertical edge joining the front and left sides shows a height of 12 centimeters. The front base edge shows a width of 3 centimeters. The right base edge shows a length of 4 centimeters. A dotted line extends diagonally from the vertex at the bottom back right side of the prism through the interior of the prism to the vertex at the top front left.
Find the length of the diagonal of the prism.
(1 point)
An illustration of a rectangular prism is shown with labeled parts. The top, front and right sides are visible. The bottom, left, and rear sides are not visible, but their positions are indicated by dashed lines. The vertical edge joining the front and left sides shows a height of 12 centimeters. The front base edge shows a width of 3 centimeters. The right base edge shows a length of 4 centimeters. A dotted line extends diagonally from the vertex at the bottom back right side of the prism through the interior of the prism to the vertex at the top front left.
Find the length of the diagonal of the prism.
(1 point)
To find the length of the diagonal of the rectangular prism, we can use the Pythagorean Theorem.
In the given illustration, we have a right triangle formed by the diagonal, the height, and the base of the prism.
Using the Pythagorean Theorem:
diagonal² = height² + width² + length²
diagonal² = 12² + 3² + 4²
diagonal² = 144 + 9 + 16
diagonal² = 169
To find the length of the diagonal, we need to take the square root of both sides:
diagonal ≈ √169 ≈ 13
Therefore, the length of the diagonal of the rectangular prism is approximately 13 centimeters.
In the given illustration, we have a right triangle formed by the diagonal, the height, and the base of the prism.
Using the Pythagorean Theorem:
diagonal² = height² + width² + length²
diagonal² = 12² + 3² + 4²
diagonal² = 144 + 9 + 16
diagonal² = 169
To find the length of the diagonal, we need to take the square root of both sides:
diagonal ≈ √169 ≈ 13
Therefore, the length of the diagonal of the rectangular prism is approximately 13 centimeters.
The Great Pyramid of Giza in Egypt has a square base with edge length of 230.5 m and a slant height of 180.2 m. Find the height of the pyramid. Round the answer to the nearest tenth.(1 point)
To find the height of the pyramid, we can use the Pythagorean Theorem.
In the given information, we have a right triangle formed by the height, half of the base, and the slant height of the pyramid.
Using the Pythagorean Theorem:
height² = slant height² - (1/2 * base)²
height² = 180.2² - (1/2 * 230.5)²
height² = 32544.04 - 13286.5625
height² = 19257.4775
To find the height, we need to take the square root of both sides:
height ≈ √19257.4775 ≈ 138.7
Therefore, the height of the pyramid is approximately 138.7 meters when rounded to the nearest tenth.
In the given information, we have a right triangle formed by the height, half of the base, and the slant height of the pyramid.
Using the Pythagorean Theorem:
height² = slant height² - (1/2 * base)²
height² = 180.2² - (1/2 * 230.5)²
height² = 32544.04 - 13286.5625
height² = 19257.4775
To find the height, we need to take the square root of both sides:
height ≈ √19257.4775 ≈ 138.7
Therefore, the height of the pyramid is approximately 138.7 meters when rounded to the nearest tenth.
Keysha is building a coffee table. It’s going to be in the shape of a rectangular prism, without the faces. She wants to make the table decorative by adding metal diagonals. The length of the coffee table will be 44 in., the width 24 in., and the height 14 in. Find the length Keysha should make each diagonal. Round the answer to the nearest tenth.(1 point)
To find the length of each diagonal, we need to calculate the diagonal of each rectangular face of the prism and the diagonal that goes through the entire rectangular prism.
The diagonal of a rectangular face can be found
The diagonal of a rectangular face can be found
Keysha is building a coffee table. It’s going to be in the shape of a rectangular prism, without the faces. She wants to make the table decorative by adding metal diagonals. The length of the coffee table will be 44 in., the width 24 in., and the height 14 in. Find the length Keysha should make each diagonal. Round the answer to the nearest tenth.(1 point)