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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)
11 answers
Based on the given information, it is not possible to determine the relationship of the sides using the Pythagorean Theorem. The Pythagorean Theorem is used to determine the relationship between the lengths of the sides in a right triangle, but the given angles (62 degrees and 28 degrees) do not indicate the presence of a right angle in the triangle.
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, 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 the other leg as x.
Using the Pythagorean Theorem, we can write:
12^2 + x^2 = 16^2
Simplifying, we have:
144 + x^2 = 256
To isolate x^2, we subtract 144 from both sides:
x^2 = 256 - 144
x^2 = 112
Taking the square root of both sides, we find:
x = √(112)
x ≈ 10.6 (rounded to the nearest tenth)
Therefore, the length of the other leg is approximately 10.6 units.
Let's denote the length of the other leg as x.
Using the Pythagorean Theorem, we can write:
12^2 + x^2 = 16^2
Simplifying, we have:
144 + x^2 = 256
To isolate x^2, we subtract 144 from both sides:
x^2 = 256 - 144
x^2 = 112
Taking the square root of both sides, we find:
x = √(112)
x ≈ 10.6 (rounded to the nearest tenth)
Therefore, the length of the other leg is approximately 10.6 units.
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)
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)
In the given scenario, we have a right triangle formed by the dashed diagonal line, the top right side of the square, and the outer right side of the square.
The length of the outer right side of the square is given as 90 feet, and the length from the stick figure to the inner right side of the square is given as 30 feet.
Let's denote the length of the dashed diagonal line as x (the distance the shortstop needs to throw the ball).
Using the Pythagorean Theorem, we can write:
x^2 = (30^2) + (90^2)
Simplifying, we have:
x^2 = 900 + 8100
x^2 = 9000
Taking the square root of both sides, we find:
x ≈ √9000
x ≈ 94.9 (rounded to the nearest tenth)
Therefore, the shortstop needs to throw the ball approximately 94.9 feet.
The length of the outer right side of the square is given as 90 feet, and the length from the stick figure to the inner right side of the square is given as 30 feet.
Let's denote the length of the dashed diagonal line as x (the distance the shortstop needs to throw the ball).
Using the Pythagorean Theorem, we can write:
x^2 = (30^2) + (90^2)
Simplifying, we have:
x^2 = 900 + 8100
x^2 = 9000
Taking the square root of both sides, we find:
x ≈ √9000
x ≈ 94.9 (rounded to the nearest tenth)
Therefore, the shortstop needs to throw the ball approximately 94.9 feet.
I got that answer as well but now I have 95 is it correct or should I go back to that orginally
If you rounded the square root of 9000 to the nearest tenth, you should have obtained approximately 94.9, as there are no decimals between 9 and 10.
However, if you rounded the answer to a whole number, it would be appropriate to round it to 95, as per typical rounding rules.
So, rounding to the nearest whole number, the correct answer would be 95 feet.
However, if you rounded the answer to a whole number, it would be appropriate to round it to 95, as per typical rounding rules.
So, rounding to the nearest whole number, the correct answer would be 95 feet.
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)
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) in quadrant 1, we can use the distance formula, which involves applying the Pythagorean theorem.
The distance formula states that the distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the given points (3, 2) and (7, 8), we can substitute the values into the distance formula:
d = √((7 - 3)^2 + (8 - 2)^2)
Simplifying:
d = √(4^2 + 6^2)
d = √(16 + 36)
d = √52
d ≈ 7.21 (rounded to the nearest hundredth)
Therefore, the length between the two points is approximately 7.21 units.
The distance formula states that the distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the given points (3, 2) and (7, 8), we can substitute the values into the distance formula:
d = √((7 - 3)^2 + (8 - 2)^2)
Simplifying:
d = √(4^2 + 6^2)
d = √(16 + 36)
d = √52
d ≈ 7.21 (rounded to the nearest hundredth)
Therefore, the length between the two points is approximately 7.21 units.
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)
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 pyramid, the height is given as 15 feet and the length of the base edge is given as 16 feet.
Let's denote the slant height as x.
Using the Pythagorean Theorem, we can write:
x^2 = 15^2 + 16^2
Simplifying, we have:
x^2 = 225 + 256
x^2 = 481
Taking the square root of both sides, we find:
x ≈ √481
x ≈ 21.95 (rounded to the nearest hundredth)
Therefore, the slant height of the square pyramid is approximately 21.95 feet.
In the pyramid, the height is given as 15 feet and the length of the base edge is given as 16 feet.
Let's denote the slant height as x.
Using the Pythagorean Theorem, we can write:
x^2 = 15^2 + 16^2
Simplifying, we have:
x^2 = 225 + 256
x^2 = 481
Taking the square root of both sides, we find:
x ≈ √481
x ≈ 21.95 (rounded to the nearest hundredth)
Therefore, the slant height of the square pyramid is approximately 21.95 feet.
7 answers