The sum of the angles in a triangle is always 180 degrees.
Therefore, if one angle is 65 degrees, the second angle can be found by subtracting 65 from 180:
180 - 65 = 115 degrees
So, the third angle in the triangle is 115 degrees.
If a right triangle has an angle that is 65°, what is the third angle in the triangle? (1 point)
35 answers
What is the measure of the exterior angle a? (1 point)
Top triangle is 37* and right bottom is 42*
Top triangle is 37* and right bottom is 42*
To determine the measure of the exterior angle, we need to use the fact that the sum of the measures of the exterior angles of any polygon is always 360 degrees.
In this case, the top triangle has an angle of 37 degrees and the right bottom triangle has an angle of 42 degrees.
We can subtract the sum of these two angles from 360 to find the measure of the exterior angle a.
360 - (37 + 42) = 281 degrees
Therefore, the measure of exterior angle a is 281 degrees.
In this case, the top triangle has an angle of 37 degrees and the right bottom triangle has an angle of 42 degrees.
We can subtract the sum of these two angles from 360 to find the measure of the exterior angle a.
360 - (37 + 42) = 281 degrees
Therefore, the measure of exterior angle a is 281 degrees.
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
In a diagram where lines S and T are parallel, when a transversal intersects the parallel lines, corresponding angles are equal.
Therefore, if one angle is labeled 22 degrees, the other three angles that will also be 22 degrees are:
1. The corresponding angle to the labeled angle
2. The alternate interior angle to the labeled angle
3. The alternate exterior angle to the labeled angle
So the other three angles that will also be 22 degrees are: 22, 22, 22.
Therefore, if one angle is labeled 22 degrees, the other three angles that will also be 22 degrees are:
1. The corresponding angle to the labeled angle
2. The alternate interior angle to the labeled angle
3. The alternate exterior angle to the labeled angle
So the other three angles that will also be 22 degrees are: 22, 22, 22.
What is the relationship of the sides in this triangle based on the Pythagorean Theorem?
N = 62*
M=28
O=?
N = 62*
M=28
O=?
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.
In this case, N = 62 degrees is an angle measurement, not a side length. Additionally, the length of one side (M = 28) is given, but O is not specified.
To find the relationship between the sides of the triangle based on the Pythagorean Theorem, we would need to know the lengths of at least two sides of the triangle.
In this case, N = 62 degrees is an angle measurement, not a side length. Additionally, the length of one side (M = 28) is given, but O is not specified.
To find the relationship between the sides of the triangle based on the Pythagorean Theorem, we would need to know the lengths of at least two sides of the triangle.
What is O and what is this answer? m^2+n^2=
Since you specified that N is an angle measurement and M is given as a length, I will assume that O refers to the length of the side opposite angle M in the right triangle.
The Pythagorean Theorem 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 hypotenuse.
Therefore, we can represent the relationship using variables as:
O^2 = M^2 + N^2
However, without knowing the length of O or the specific values of M and N, I cannot provide a numerical value for O or solve the equation.
The Pythagorean Theorem 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 hypotenuse.
Therefore, we can represent the relationship using variables as:
O^2 = M^2 + N^2
However, without knowing the length of O or the specific values of M and N, I cannot provide a numerical value for O or solve the equation.
The triangles right top side is 62* and the bottom is 28 what is the left top one and what is the answer or this m^2 + n^2=
If the right top side of the triangle is 62 degrees and the bottom side is 28 units long, we can use the Pythagorean Theorem to find the length of the left top side, which I'll call 'O'.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two legs (the sides that form the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
Using this theorem in this scenario, we have:
O^2 = (M^2) + (N^2)
O^2 = (28^2) + (62^2)
To solve for O, we need to calculate 28^2 and 62^2, and then take their sum before finding the square root of the result:
O^2 = 784 + 3,844
O^2 = 4,628
O ≈ √4,628
O ≈ 68.04
Therefore, the length of the left top side (O) is approximately 68.04 units.
The equation m^2 + n^2 = 4,628 represents the relationship between the squares of the lengths of the sides of this right triangle.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two legs (the sides that form the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
Using this theorem in this scenario, we have:
O^2 = (M^2) + (N^2)
O^2 = (28^2) + (62^2)
To solve for O, we need to calculate 28^2 and 62^2, and then take their sum before finding the square root of the result:
O^2 = 784 + 3,844
O^2 = 4,628
O ≈ √4,628
O ≈ 68.04
Therefore, the length of the left top side (O) is approximately 68.04 units.
The equation m^2 + n^2 = 4,628 represents the relationship between the squares of the lengths of the sides of this right triangle.
If a triangle has sides measuring 60, 75, and 45, is it a right triangle? (1 point)
To determine if a triangle is 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 (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
If we have a triangle with sides measuring 60, 75, and 45, we can check if it satisfies the Pythagorean Theorem:
60^2 + 45^2 = 3600 + 2025 = 5625
75^2 = 5625
Since the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse), this triangle satisfies the Pythagorean Theorem.
Therefore, the given triangle with sides measuring 60, 75, and 45 is a right triangle.
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.
If we have a triangle with sides measuring 60, 75, and 45, we can check if it satisfies the Pythagorean Theorem:
60^2 + 45^2 = 3600 + 2025 = 5625
75^2 = 5625
Since the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse), this triangle satisfies the Pythagorean Theorem.
Therefore, the given triangle with sides measuring 60, 75, and 45 is a right triangle.
If a triangle has sides measuring 60, 75, and 45, is it a right triangle? (1 point)
• No, because 5,625 does not equal 3,600.
• Yes, because 3,600 equals 3,600.
• No, because 9,225 does not equal 2,025.
• Yes, because 5,625 equals 5,625.
• No, because 5,625 does not equal 3,600.
• Yes, because 3,600 equals 3,600.
• No, because 9,225 does not equal 2,025.
• Yes, because 5,625 equals 5,625.
If a triangle has sides measuring 60, 75, and 45, it is not a right triangle.
What is the answer out of those I gave you
The correct answer out of the options you gave is:
• No, because 5,625 does not equal 3,600.
• 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. (1 point)
To determine if the triangle DEF is a right triangle, we can use the Pythagorean Theorem.
According to the Pythagorean 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 the sides 50, 40, and 32 satisfy the Pythagorean Theorem:
50^2 = 2500
40^2 + 32^2 = 1600 + 1024 = 2624
Since 2500 is not equal to 2624, the sides do not satisfy the Pythagorean Theorem.
Therefore, triangle DEF is not a right triangle, and the answer would be 0.
According to the Pythagorean 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 the sides 50, 40, and 32 satisfy the Pythagorean Theorem:
50^2 = 2500
40^2 + 32^2 = 1600 + 1024 = 2624
Since 2500 is not equal to 2624, the sides do not satisfy the Pythagorean Theorem.
Therefore, triangle DEF is not a right triangle, and the answer would be 0.
If a triangle has sides of length 12 and 16, how long is the hypotenuse? (1 point)
To determine the length of the hypotenuse in a right triangle given the lengths of the other two sides, 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 other two sides.
In this case, let's denote the length of the hypotenuse as 'c', and the lengths of the other two sides as 12 and 16.
According to the Pythagorean Theorem:
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
To find the length of the hypotenuse, we take the square root of both sides of the equation:
c = √400
c = 20
Therefore, the length of the hypotenuse is 20 units.
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, let's denote the length of the hypotenuse as 'c', and the lengths of the other two sides as 12 and 16.
According to the Pythagorean Theorem:
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
To find the length of the hypotenuse, we take the square root of both sides of the equation:
c = √400
c = 20
Therefore, the length of the hypotenuse is 20 units.
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 solve for the length of the other leg in a right triangle, given the length of one leg and the hypotenuse, we can use the Pythagorean Theorem.
According to the Pythagorean Theorem, 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'. We have:
x^2 + 12^2 = 16^2
x^2 + 144 = 256
x^2 = 112
Taking the square root of both sides, we find:
x = √112
Using a calculator or simplifying the square root, we obtain:
x ≈ 10.6 (rounded to the nearest tenth)
Therefore, the length of the other leg is approximately 10.6 units.
According to the Pythagorean Theorem, 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'. We have:
x^2 + 12^2 = 16^2
x^2 + 144 = 256
x^2 = 112
Taking the square root of both sides, we find:
x = √112
Using a calculator or simplifying the square root, we obtain:
x ≈ 10.6 (rounded to the nearest tenth)
Therefore, the length of the other leg is approximately 10.6 units.
A shortstop is standing in the base path between second and third base when she fields the bail. 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 third base would be the same as the distance from second base to first base.
Therefore, the shortstop needs to throw the ball a distance of 30 feet to reach first base.
Therefore, the shortstop needs to throw the ball a distance of 30 feet to reach first base.
Find the slant height of the square pyramid.
(1 point)
Width 16
Height 15
(1 point)
Width 16
Height 15
To find the slant height of a square pyramid, we can use the Pythagorean Theorem.
The slant height (l) of a square pyramid can be found by using the height (h) and the base width (w) of the pyramid.
In this case, the width of the square base is given as 16 and the height of the pyramid is given as 15.
Since the slant height forms a right triangle with the height and half the base width, we can use the Pythagorean Theorem:
l^2 = h^2 + (w/2)^2
l^2 = 15^2 + (16/2)^2
l^2 = 225 + 64
l^2 = 289
Taking the square root of both sides, we find:
l = √289
l = 17
Therefore, the slant height of the square pyramid is 17 units.
The slant height (l) of a square pyramid can be found by using the height (h) and the base width (w) of the pyramid.
In this case, the width of the square base is given as 16 and the height of the pyramid is given as 15.
Since the slant height forms a right triangle with the height and half the base width, we can use the Pythagorean Theorem:
l^2 = h^2 + (w/2)^2
l^2 = 15^2 + (16/2)^2
l^2 = 225 + 64
l^2 = 289
Taking the square root of both sides, we find:
l = √289
l = 17
Therefore, the slant height of the square pyramid is 17 units.
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.
The height (h) of the pyramid forms a right triangle with half the base width (w/2) and the slant height (l).
In this case, the base width of the square pyramid is given as 230.5 m, and the slant height is given as 180.2 m.
Using the Pythagorean Theorem, we have:
h^2 = l^2 - (w/2)^2
h^2 = (180.2)^2 - (230.5/2)^2
h^2 = 32544.04 - 13295.0625
h^2 = 19248.9775
Taking the square root of both sides, we find:
h = √19248.9775
h ≈ 138.8
Therefore, the height of the pyramid is approximately 138.8 meters.
The height (h) of the pyramid forms a right triangle with half the base width (w/2) and the slant height (l).
In this case, the base width of the square pyramid is given as 230.5 m, and the slant height is given as 180.2 m.
Using the Pythagorean Theorem, we have:
h^2 = l^2 - (w/2)^2
h^2 = (180.2)^2 - (230.5/2)^2
h^2 = 32544.04 - 13295.0625
h^2 = 19248.9775
Taking the square root of both sides, we find:
h = √19248.9775
h ≈ 138.8
Therefore, the height of the pyramid is approximately 138.8 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 the diagonal in a rectangular prism, we can use the Pythagorean Theorem.
In this case, the rectangular prism represents the coffee table, and we want to find the length of the metal diagonals.
The length (l), width (w), and height (h) of the coffee table are given as 44 in., 24 in., and 14 in., respectively.
To find the length of each diagonal, we can use the Pythagorean Theorem in each of the three dimensions of the rectangular prism.
For the first diagonal:
d1^2= l^2 + w^2
d1^2= 44^2 + 24^2
d1^2= 1936 + 576
d1^2= 2512
For the second diagonal:
d2^2= l^2 + h^2
d2^2= 44^2 + 14^2
d2^2= 1936 + 196
d2^2= 2132
For the third diagonal:
d3^2= w^2 + h^2
d3^2= 24^2 + 14^2
d3^2= 576 + 196
d3^2= 772
Taking the square root of each diagonal, we find:
d1 ≈ 50.1 in.
d2 ≈ 46.2 in.
d3 ≈ 27.8 in.
Therefore, Keysha should make each diagonal approximately 50.1 in., 46.2 in., and 27.8 in. in length.
In this case, the rectangular prism represents the coffee table, and we want to find the length of the metal diagonals.
The length (l), width (w), and height (h) of the coffee table are given as 44 in., 24 in., and 14 in., respectively.
To find the length of each diagonal, we can use the Pythagorean Theorem in each of the three dimensions of the rectangular prism.
For the first diagonal:
d1^2= l^2 + w^2
d1^2= 44^2 + 24^2
d1^2= 1936 + 576
d1^2= 2512
For the second diagonal:
d2^2= l^2 + h^2
d2^2= 44^2 + 14^2
d2^2= 1936 + 196
d2^2= 2132
For the third diagonal:
d3^2= w^2 + h^2
d3^2= 24^2 + 14^2
d3^2= 576 + 196
d3^2= 772
Taking the square root of each diagonal, we find:
d1 ≈ 50.1 in.
d2 ≈ 46.2 in.
d3 ≈ 27.8 in.
Therefore, Keysha should make each diagonal approximately 50.1 in., 46.2 in., and 27.8 in. in length.
So what’s the answer
The answer is:
Keysha should make each diagonal approximately 50.1 inches, 46.2 inches, and 27.8 inches in length.
Keysha should make each diagonal approximately 50.1 inches, 46.2 inches, and 27.8 inches in length.
Explain a proof of the Pythagorean Theorem using the image.
I apologize, but as a text-based AI model, I am unable to view or interpret images. However, I can provide you with a verbal explanation of a common proof of the Pythagorean Theorem.
One common proof is the geometric proof, which involves using the areas of squares. It goes as follows:
Consider a right triangle ABC, where the right angle is at C.
Draw squares on each side of the triangle. Let's label the sides of the triangle a, b, and c, where c is the hypotenuse.
First, draw a square with side length a, and place it above the triangle, such that one side of the square coincides with side AB of the triangle.
Next, draw another square with side length b, and place it to the right of the triangle, such that one side of the square coincides with side BC of the triangle.
Now, draw a third square with side length c, and place it adjacent to the other two squares.
The area of the square with side length c is equal to the sum of the areas of the squares with side lengths a and b.
Mathematically, this can be expressed as:
c^2 = a^2 + b^2
This is 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.
Thus, by using the areas of the squares, we can prove the Pythagorean Theorem.
Apologies again for not being able to provide a visual interpretation.
One common proof is the geometric proof, which involves using the areas of squares. It goes as follows:
Consider a right triangle ABC, where the right angle is at C.
Draw squares on each side of the triangle. Let's label the sides of the triangle a, b, and c, where c is the hypotenuse.
First, draw a square with side length a, and place it above the triangle, such that one side of the square coincides with side AB of the triangle.
Next, draw another square with side length b, and place it to the right of the triangle, such that one side of the square coincides with side BC of the triangle.
Now, draw a third square with side length c, and place it adjacent to the other two squares.
The area of the square with side length c is equal to the sum of the areas of the squares with side lengths a and b.
Mathematically, this can be expressed as:
c^2 = a^2 + b^2
This is 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.
Thus, by using the areas of the squares, we can prove the Pythagorean Theorem.
Apologies again for not being able to provide a visual interpretation.