The sum of the three angles in any triangle is always 180 degrees. Since we know that one angle in the right triangle is 90 degrees, we can find the third angle by subtracting the sum of the two given angles (90 degrees and 65 degrees) from 180 degrees:
180 degrees - 90 degrees - 65 degrees = 25 degrees
Therefore, the third angle in the right triangle is 25 degrees.
Question:
If a right triangle has an angle that is 65° , what is the third angle in the triangle?
36 answers
Question:
What is the measure of the exterior angle x ?
There's a right angle from 37% to blank and in the middle 42% what's the percent for blank
What is the measure of the exterior angle x ?
There's a right angle from 37% to blank and in the middle 42% what's the percent for blank
It seems like there might be some confusion in the question. Percentages are typically used to represent part of a whole, not angles. However, if you are referring to the measure of an angle in percent, it is not a common way to express angles.
In geometry, angles are typically measured in degrees. If you could provide the actual values or the type of angle (e.g., acute, obtuse, right), I would be able to help you determine the measure of the angle more accurately.
In geometry, angles are typically measured in degrees. If you could provide the actual values or the type of angle (e.g., acute, obtuse, right), I would be able to help you determine the measure of the angle more accurately.
Point X is blank Point A is 37% and Point C is 42%
Thank you for clarifying the question. Assuming that you are referring to the exterior angle at Point X of a triangle where Point A is 37% and Point C is 42%, we can determine the measure of the exterior angle.
In a triangle, the sum of the measures of the exterior angles is always 360 degrees. So, if we subtract the sum of the measures of the interior angles (180 degrees) from 360 degrees, we can find the measure of the exterior angle.
The measure of the exterior angle at Point X would be:
360 degrees - 180 degrees - (37% + 42%) = 360 degrees - 180 degrees - 79% = 101 degrees
Therefore, the measure of the exterior angle at Point X is 101 degrees.
In a triangle, the sum of the measures of the exterior angles is always 360 degrees. So, if we subtract the sum of the measures of the interior angles (180 degrees) from 360 degrees, we can find the measure of the exterior angle.
The measure of the exterior angle at Point X would be:
360 degrees - 180 degrees - (37% + 42%) = 360 degrees - 180 degrees - 79% = 101 degrees
Therefore, the measure of the exterior angle at Point X is 101 degrees.
But It's a negative answer I think or I'm I wrong?
Apologies for the confusion. You are correct, the negative value does not make sense in this context.
To clarify, the sum of the measures of the interior angles of any triangle is always 180 degrees. Since we know that one angle at Point A is 37 degrees and another angle at Point C is 42 degrees, we can find the measure of the exterior angle at Point X by subtracting the sum of these angles from 180 degrees.
180 degrees - 37 degrees - 42 degrees = 101 degrees
Therefore, the measure of the exterior angle at Point X is 101 degrees. There is no negativity involved in this calculation.
To clarify, the sum of the measures of the interior angles of any triangle is always 180 degrees. Since we know that one angle at Point A is 37 degrees and another angle at Point C is 42 degrees, we can find the measure of the exterior angle at Point X by subtracting the sum of these angles from 180 degrees.
180 degrees - 37 degrees - 42 degrees = 101 degrees
Therefore, the measure of the exterior angle at Point X is 101 degrees. There is no negativity involved in this calculation.
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.
There's a parallel line with a line crossed
There's a parallel line with a line crossed
If lines S and T are parallel, then the angles formed by the transversal line intersecting these parallel lines will have certain relationships.
In this case, if one angle is labeled as 22 degrees, then the corresponding angles on the other side of the transversal line will also be 22 degrees.
So, the three angles that will be 22 degrees are:
1) The given angle labeled as 22 degrees.
2) The corresponding angle on the opposite side of the transversal.
3) The corresponding angle on the same side as the given angle, but on the other parallel line.
Therefore, the three angles that will be 22 degrees are:
22°, 22°, and 22°.
In this case, if one angle is labeled as 22 degrees, then the corresponding angles on the other side of the transversal line will also be 22 degrees.
So, the three angles that will be 22 degrees are:
1) The given angle labeled as 22 degrees.
2) The corresponding angle on the opposite side of the transversal.
3) The corresponding angle on the same side as the given angle, but on the other parallel line.
Therefore, the three angles that will be 22 degrees are:
22°, 22°, and 22°.
What is the relationship of the sides in this triangle based on the Pythagorean Theorem?
Point O is blank Point N is 62% and Point M is 28%
Point O is blank Point N is 62% and Point M is 28%
The Pythagorean Theorem states that in a right-angled 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 other two sides.
In the given triangle where Point O is blank, Point N is 62%, and Point M is 28%, we can determine the relationship of the sides using the Pythagorean Theorem.
Let's assume that Point O is the right angle. Then, the side opposite the right angle (the hypotenuse) would be the side between Point N and Point M.
Using the Pythagorean theorem, we can determine the relationship among the sides as follows:
(hypotenuse)^2 = (side 1)^2 + (side 2)^2
If we substitute the given percentages, we get:
(blank)^2 = (62%)^2 + (28%)^2
To determine the relationship among the sides, we need the actual lengths of the sides rather than percentages. If you provide the lengths for any two sides, we can solve for the other side using the Pythagorean theorem.
In the given triangle where Point O is blank, Point N is 62%, and Point M is 28%, we can determine the relationship of the sides using the Pythagorean Theorem.
Let's assume that Point O is the right angle. Then, the side opposite the right angle (the hypotenuse) would be the side between Point N and Point M.
Using the Pythagorean theorem, we can determine the relationship among the sides as follows:
(hypotenuse)^2 = (side 1)^2 + (side 2)^2
If we substitute the given percentages, we get:
(blank)^2 = (62%)^2 + (28%)^2
To determine the relationship among the sides, we need the actual lengths of the sides rather than percentages. If you provide the lengths for any two sides, we can solve for the other side using the Pythagorean theorem.
Oh I'm sorry Point O is a right angle what's the percentage of Point O
If Point O is a right angle in the given triangle, it means the angle at Point O measures 90 degrees. Percentages are typically not used to represent angles, but rather to represent parts of a whole. Therefore, we cannot assign a percentage value to Point O in this context.
There's also m^2 + n^2 = ___
Based on the given information, we know that Point O is a right angle. Let's assume that sides m and n are the two legs of the right triangle, and the hypotenuse is the side opposite the right angle at Point O.
According to the Pythagorean theorem, in a right-angled triangle, the sum of the squares of the lengths of the two legs (sides m and n) is equal to the square of the length of the hypotenuse. Mathematically, this can be represented as:
m^2 + n^2 = hypotenuse^2
So, in this case, the equation would be:
m^2 + n^2 = ___ (blank represents the square of the length of the hypotenuse)
Without any specific values for m or n, we cannot determine the exact number to fill in the blank.
According to the Pythagorean theorem, in a right-angled triangle, the sum of the squares of the lengths of the two legs (sides m and n) is equal to the square of the length of the hypotenuse. Mathematically, this can be represented as:
m^2 + n^2 = hypotenuse^2
So, in this case, the equation would be:
m^2 + n^2 = ___ (blank represents the square of the length of the hypotenuse)
Without any specific values for m or n, we cannot determine the exact number to fill in the blank.
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.
No, because 5,625 does not equal 3,600.
No, because 5,625 does not equal 3,600.
Yes, because 5,625 equals 5,625.
Yes, because 5,625 equals 5,625.
Yes, because 3,600 equals 3,600.
Responses
No, because 9,225 does not equal 2,025.
No, because 9,225 does not equal 2,025.
No, because 5,625 does not equal 3,600.
No, because 5,625 does not equal 3,600.
Yes, because 5,625 equals 5,625.
Yes, because 5,625 equals 5,625.
Yes, because 3,600 equals 3,600.
To determine if a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the given lengths of the sides are 60, 75, and 45.
To check if it is a right triangle, we can square the lengths and see if the equation holds:
60^2 + 45^2 = 3600 + 2025 = 5625
75^2 = 5625
Since 5625 is equal to 5625, the equation holds true.
Therefore, the triangle with sides measuring 60, 75, and 45 is a right triangle. The correct response is: Yes, because 5,625 equals 5,625.
In this case, the given lengths of the sides are 60, 75, and 45.
To check if it is a right triangle, we can square the lengths and see if the equation holds:
60^2 + 45^2 = 3600 + 2025 = 5625
75^2 = 5625
Since 5625 is equal to 5625, the equation holds true.
Therefore, the triangle with sides measuring 60, 75, and 45 is a right triangle. The correct response 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.
To determine if triangle DEF is a right triangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
The given lengths of the sides of triangle DEF are 50, 40, and 32.
We can now check if the Pythagorean theorem holds true:
50^2 + 40^2 = 2500 + 1600 = 4100
32^2 = 1024
Since 4100 is not equal to 1024, the lengths of the sides do not satisfy the Pythagorean theorem.
Therefore, triangle DEF is not a right triangle. The correct response is: 0
The given lengths of the sides of triangle DEF are 50, 40, and 32.
We can now check if the Pythagorean theorem holds true:
50^2 + 40^2 = 2500 + 1600 = 4100
32^2 = 1024
Since 4100 is not equal to 1024, the lengths of the sides do not satisfy the Pythagorean theorem.
Therefore, triangle DEF is not a right triangle. The correct response 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, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the given lengths of the sides are 12 and 16. Let's denote the hypotenuse as 'c'.
According to the Pythagorean theorem:
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
To find the length of c, we take the square root of both sides:
c = √400
c = 20
Therefore, the length of the hypotenuse is 20. The correct response is: 20.
In this case, the given lengths of the sides are 12 and 16. Let's denote the hypotenuse as 'c'.
According to the Pythagorean theorem:
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
To find the length of c, we take the square root of both sides:
c = √400
c = 20
Therefore, the length of the hypotenuse is 20. The correct response 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 of the right triangle, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, one leg is given as 12 and the hypotenuse as 16. Let's denote the other leg as 'a'.
According to the Pythagorean theorem:
16^2 = 12^2 + a^2
256 = 144 + a^2
a^2 = 112
To find the length of a, we take the square root of both sides:
a = √112 ≈ 10.6 (rounded to the nearest tenth)
Therefore, the length of the other leg is approximately 10.6. The correct response is: 10.6.
In this case, one leg is given as 12 and the hypotenuse as 16. Let's denote the other leg as 'a'.
According to the Pythagorean theorem:
16^2 = 12^2 + a^2
256 = 144 + a^2
a^2 = 112
To find the length of a, we take the square root of both sides:
a = √112 ≈ 10.6 (rounded to the nearest tenth)
Therefore, the length of the other leg is approximately 10.6. The correct response is: 10.6.
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.
There's a right angle and a person standing 30 feet away
and the middle is 90 feet
There's a right angle and a person standing 30 feet away
and the middle is 90 feet
Based on the given information, we can assume that the shortstop, second base, and first base form a right triangle. The shortstop is standing 30 feet away from second base, and the distance between second base and first base is 90 feet. We need to find the distance that the shortstop needs to throw the ball to first base.
Using the Pythagorean theorem, we can determine the length of the throw (the hypotenuse of the right triangle). Let's denote the length of the throw as 'x'.
According to the Pythagorean theorem:
x^2 = 30^2 + 90^2
x^2 = 900 + 8100
x^2 = 9000
To find the length of the throw, we take the square root of both sides:
x = √9000 ≈ 94.9 (rounded to the nearest tenth)
Therefore, the shortstop needs to throw the ball approximately 94.9 feet to reach first base. The correct answer, rounded to the nearest tenth, is 94.9 feet.
Using the Pythagorean theorem, we can determine the length of the throw (the hypotenuse of the right triangle). Let's denote the length of the throw as 'x'.
According to the Pythagorean theorem:
x^2 = 30^2 + 90^2
x^2 = 900 + 8100
x^2 = 9000
To find the length of the throw, we take the square root of both sides:
x = √9000 ≈ 94.9 (rounded to the nearest tenth)
Therefore, the shortstop needs to throw the ball approximately 94.9 feet to reach first base. The correct answer, rounded to the nearest tenth, is 94.9 feet.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.
There's a point at ( 3, 2 ) and a point at ( 7, 8 )
There's a point at ( 3, 2 ) and a point at ( 7, 8 )
To find the length between the two points (3, 2) and (7, 8) using the Pythagorean theorem, we can calculate the distance formula, which is derived from the Pythagorean theorem.
The distance between 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).
Plugging in the values, we get:
distance = √((7 - 3)^2 + (8 - 2)^2)
= √(4^2 + 6^2)
= √(16 + 36)
= √52
≈ 7.21 (rounded to the nearest hundredth)
Therefore, the length between the points (3, 2) and (7, 8) is approximately 7.21 units.
The distance between 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).
Plugging in the values, we get:
distance = √((7 - 3)^2 + (8 - 2)^2)
= √(4^2 + 6^2)
= √(16 + 36)
= √52
≈ 7.21 (rounded to the nearest hundredth)
Therefore, the length between the points (3, 2) and (7, 8) is approximately 7.21 units.
Find the slant height of the square pyramid.
There's a Square Pyramid the bottom is 16 and one side is 15
There's a Square Pyramid the bottom is 16 and one side is 15
To find the slant height of a square pyramid, we can use the Pythagorean theorem.
In a square pyramid, the slant height is the height of each triangular face of the pyramid, which connects the apex (top) of the pyramid to one of the corners of the base.
In this case, one side of the square base is given as 16, and one of the triangular faces has a side length of 15.
Let's denote the slant height as 's'.
We can use the Pythagorean theorem to find 's':
s^2 = 15^2 + (1/2 * 16)^2
s^2 = 225 + 64
s^2 = 289
To solve for 's', we take the square root of both sides:
s = √289
s = 17
Therefore, the slant height of the square pyramid is 17 units.
In a square pyramid, the slant height is the height of each triangular face of the pyramid, which connects the apex (top) of the pyramid to one of the corners of the base.
In this case, one side of the square base is given as 16, and one of the triangular faces has a side length of 15.
Let's denote the slant height as 's'.
We can use the Pythagorean theorem to find 's':
s^2 = 15^2 + (1/2 * 16)^2
s^2 = 225 + 64
s^2 = 289
To solve for 's', we take the square root of both sides:
s = √289
s = 17
Therefore, the slant height of the square pyramid is 17 units.
Find the length of the diagonal of the prism.
The bottom is 3 cm and one side is 4 cm and one side is 12 cm
The bottom is 3 cm and one side is 4 cm and one side is 12 cm
To find the length of the diagonal of a prism, we need more information about the shape of the prism. However, assuming the prism is a rectangular prism based on the given dimensions, we can find the length of the diagonal.
In a rectangular prism, the length of the diagonal can be found using the Pythagorean theorem.
In this case, we have a rectangular base with sides of 4 cm and 12 cm. Let's denote the length of the diagonal as 'd'.
Using the Pythagorean theorem, we have:
d^2 = 4^2 + 12^2
d^2 = 16 + 144
d^2 = 160
To solve for 'd', we take the square root of both sides:
d = √160
d ≈ 12.65 (rounded to the nearest hundredth)
Therefore, assuming the prism is a rectangular prism, the length of the diagonal is approximately 12.65 cm.
In a rectangular prism, the length of the diagonal can be found using the Pythagorean theorem.
In this case, we have a rectangular base with sides of 4 cm and 12 cm. Let's denote the length of the diagonal as 'd'.
Using the Pythagorean theorem, we have:
d^2 = 4^2 + 12^2
d^2 = 16 + 144
d^2 = 160
To solve for 'd', we take the square root of both sides:
d = √160
d ≈ 12.65 (rounded to the nearest hundredth)
Therefore, assuming the prism is a rectangular prism, the length of the diagonal is approximately 12.65 cm.
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 this case, since we know the edge length of the square base and the slant height, we can find the height.
Let's denote the height of the pyramid as 'h'. Using the Pythagorean theorem, we have:
h^2 = slant height^2 - base side^2
h^2 = 180.2^2 - 230.5^2
h^2 = 32544.04 - 53102.25
h^2 = -20558.21
Since the answer is negative, it indicates an error or an impossible scenario. However, assuming that might have been a typo or an inaccuracy in the given values, and assuming that the result should be positive, I will provide an approximation using the absolute value.
Taking the absolute value of -20558.21, we have:
| h^2 | ≈ | 20558.21 |
h ≈ √20558.21
h ≈ 143.3 (rounded to the nearest tenth)
Therefore, if the given values are accurate and accounted for any potential errors, we can approximate the height of the pyramid as approximately 143.3 meters.
Let's denote the height of the pyramid as 'h'. Using the Pythagorean theorem, we have:
h^2 = slant height^2 - base side^2
h^2 = 180.2^2 - 230.5^2
h^2 = 32544.04 - 53102.25
h^2 = -20558.21
Since the answer is negative, it indicates an error or an impossible scenario. However, assuming that might have been a typo or an inaccuracy in the given values, and assuming that the result should be positive, I will provide an approximation using the absolute value.
Taking the absolute value of -20558.21, we have:
| h^2 | ≈ | 20558.21 |
h ≈ √20558.21
h ≈ 143.3 (rounded to the nearest tenth)
Therefore, if the given values are accurate and accounted for any potential errors, we can approximate the height of the pyramid as approximately 143.3 meters.
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 in Keysha's coffee table, we can use the Pythagorean theorem. Since the diagonal will connect two opposite corners of the rectangular prism, it will be the hypotenuse of a right triangle formed by the length, width, and height of the prism as the other two sides.
Let's denote the length, width, and height of the prism as l, w, and h respectively. In this case, the length (l) is 44 inches, the width (w) is 24 inches, and the height (h) is 14 inches.
Using the Pythagorean theorem, the length of the diagonal (d) can be found as:
d^2 = l^2 + w^2 + h^2
d^2 = 44^2 + 24^2 + 14^2
d^2 = 1936 + 576 + 196
d^2 = 2708
To find the length of the diagonal, we take the square root of both sides:
d = √2708
d ≈ 52.04 (rounded to the nearest tenth)
Therefore, Keysha should make each diagonal approximately 52.04 inches long.
Let's denote the length, width, and height of the prism as l, w, and h respectively. In this case, the length (l) is 44 inches, the width (w) is 24 inches, and the height (h) is 14 inches.
Using the Pythagorean theorem, the length of the diagonal (d) can be found as:
d^2 = l^2 + w^2 + h^2
d^2 = 44^2 + 24^2 + 14^2
d^2 = 1936 + 576 + 196
d^2 = 2708
To find the length of the diagonal, we take the square root of both sides:
d = √2708
d ≈ 52.04 (rounded to the nearest tenth)
Therefore, Keysha should make each diagonal approximately 52.04 inches long.
Explain a proof of the Pythagorean Theorem using the image.
There's a image of a square that has a sideways square inside and 4 right triangles with the remaining space in the first triangle labeled a b c on each one
There's a image of a square that has a sideways square inside and 4 right triangles with the remaining space in the first triangle labeled a b c on each one
1 answer