Question
A right triangle has an angle that is 36°
. What is the measure of the third angle in this triangle?(1 point)
Responses
There is not enough information to find the third angle.
There is not enough information to find the third angle.
90°
90 degrees
126°
126 degrees
54°
. What is the measure of the third angle in this triangle?(1 point)
Responses
There is not enough information to find the third angle.
There is not enough information to find the third angle.
90°
90 degrees
126°
126 degrees
54°
Answers
Answer
An illustration shows a triangle with a 90 degree angle at the top vertex. The interior angle of the left vertex is labeled x. A line extending outward from the right vertex forms an exterior angle of 152 degrees.
Find angle x
.
(1 point)
Responses
62°
62 degrees
28°
28 degrees
90°
90 degrees
118°
Answer
.
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.
Side m
is approximately 6.1 units, side n
is approximately 11.48 units, and side o
is 13 units. What is the length of the hypotenuse of this triangle? How do you know?
(1 point)
Responses
The length is approximately 11.48 units because it is the middle length.
The length is approximately 11.48 units because it is the middle length.
The length is 13 units because the hypotenuse is the longest side.
The length is 13 units because the hypotenuse is the longest side.
The length is approximately 6.1 units because the hypotenuse is the shortest side.
The length is approximately 6.1 units because the hypotenuse is the shortest side.
The length is approximately 11.48 units because it forms the right angle.
The length is approximately 11.48 units because it forms the right angle.
Remaining Attempts : 3
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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.
Side m
is approximately 6.1 units, side n
is approximately 11.48 units, and side o
is 13 units. What is the length of the hypotenuse of this triangle? How do you know?
(1 point)
Responses
The length is approximately 11.48 units because it is the middle length.
The length is approximately 11.48 units because it is the middle length.
The length is 13 units because the hypotenuse is the longest side.
The length is 13 units because the hypotenuse is the longest side.
The length is approximately 6.1 units because the hypotenuse is the shortest side.
The length is approximately 6.1 units because the hypotenuse is the shortest side.
The length is approximately 11.48 units because it forms the right angle.
The length is approximately 11.48 units because it forms the right angle.
Remaining Attempts : 3
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Answer
If triangle ABC
has sides measuring 39, 15, and 36, is the triangle a right triangle?(1 point)
Responses
No, because the sum of the squared legs do not equal the square root of the hypotenuse.
No, because the sum of the squared legs do not equal the square root of the hypotenuse.
No, because 392+152≠362
No, because 39 squared plus 15 squared not equal to 36 squared
Yes, because 1,521 equals 1,521.
Yes, because 1,521 equals 1,521.
Yes, because 1,746 equals 1,746.
has sides measuring 39, 15, and 36, is the triangle a right triangle?(1 point)
Responses
No, because the sum of the squared legs do not equal the square root of the hypotenuse.
No, because the sum of the squared legs do not equal the square root of the hypotenuse.
No, because 392+152≠362
No, because 39 squared plus 15 squared not equal to 36 squared
Yes, because 1,521 equals 1,521.
Yes, because 1,521 equals 1,521.
Yes, because 1,746 equals 1,746.
Answer
Can a triangle with sides 7, 10, and 12 be a right triangle? How do you know?(1 point)
Responses
There is no way to tell without an angle measure.
There is no way to tell without an angle measure.
No, because 193 does not equal 100.
No, because 193 does not equal 100.
No, because 149 does not equal 144.
No, because 149 does not equal 144.
Yes, because it looks like a right triangle.
Responses
There is no way to tell without an angle measure.
There is no way to tell without an angle measure.
No, because 193 does not equal 100.
No, because 193 does not equal 100.
No, because 149 does not equal 144.
No, because 149 does not equal 144.
Yes, because it looks like a right triangle.
Answered by
GPT-4o mini
In a right triangle, one angle is always 90°. The sum of the angles in any triangle is 180°. Therefore, to find the third angle, we can use the following calculation:
1. The sum of the angles in a triangle is 180°.
2. One angle is 90° (the right angle).
3. Another angle is given as 36°.
So, the third angle can be calculated as follows:
\[
\text{Third angle} = 180° - 90° - 36° = 54°
\]
Thus, the measure of the third angle in this triangle is **54°**.
1. The sum of the angles in a triangle is 180°.
2. One angle is 90° (the right angle).
3. Another angle is given as 36°.
So, the third angle can be calculated as follows:
\[
\text{Third angle} = 180° - 90° - 36° = 54°
\]
Thus, the measure of the third angle in this triangle is **54°**.
Answered by
GPT-4o mini
In this problem, we are given a triangle with a right angle (90°) at the top vertex and an exterior angle of 152° at the right vertex. We need to find the angle \(x\) at the left vertex.
By the exterior angle theorem, the exterior angle is equal to the sum of the two non-adjacent interior angles. In this case, the exterior angle (152°) is equal to the angle at the left vertex (\(x\)) plus the right angle (90°).
So, we can set up the equation:
\[
152° = x + 90°
\]
To find \(x\), we can rearrange the equation:
\[
x = 152° - 90°
\]
\[
x = 62°
\]
Thus, the measure of angle \(x\) is **62°**.
By the exterior angle theorem, the exterior angle is equal to the sum of the two non-adjacent interior angles. In this case, the exterior angle (152°) is equal to the angle at the left vertex (\(x\)) plus the right angle (90°).
So, we can set up the equation:
\[
152° = x + 90°
\]
To find \(x\), we can rearrange the equation:
\[
x = 152° - 90°
\]
\[
x = 62°
\]
Thus, the measure of angle \(x\) is **62°**.
Answered by
GPT-4o mini
In a triangle, the hypotenuse is defined as the longest side, which is opposite the right angle. In this case, we need to identify the angles and sides.
You have provided the following information:
- Angle \(N\) measures 62 degrees
- Angle \(M\) measures 28 degrees
- Therefore, angle \(O\) can be calculated as follows:
\[
\text{Angle } O = 180° - 62° - 28° = 90°
\]
This indicates that the triangle \(MNO\) is a right triangle, with angle \(O\) being the right angle.
Since angle \(O\) is the right angle, the hypotenuse of this triangle will be the side opposite to angle \(O\), which is side \(n\).
You mentioned that:
- Side \(m\) is approximately 6.1 units
- Side \(n\) is approximately 11.48 units
- Side \(o\) is 13 units
Given that \(o\) is the side opposite the right angle (hypotenuse):
The correct response is:
**The length is 13 units because the hypotenuse is the longest side.**
You have provided the following information:
- Angle \(N\) measures 62 degrees
- Angle \(M\) measures 28 degrees
- Therefore, angle \(O\) can be calculated as follows:
\[
\text{Angle } O = 180° - 62° - 28° = 90°
\]
This indicates that the triangle \(MNO\) is a right triangle, with angle \(O\) being the right angle.
Since angle \(O\) is the right angle, the hypotenuse of this triangle will be the side opposite to angle \(O\), which is side \(n\).
You mentioned that:
- Side \(m\) is approximately 6.1 units
- Side \(n\) is approximately 11.48 units
- Side \(o\) is 13 units
Given that \(o\) is the side opposite the right angle (hypotenuse):
The correct response is:
**The length is 13 units because the hypotenuse is the longest side.**
Answered by
GPT-4o mini
To determine if triangle ABC with sides measuring 39, 15, and 36 is a right triangle, we should apply the Pythagorean theorem. According to the theorem, a triangle is a right triangle if the square of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides (the legs).
Here, the sides are:
- \(a = 15\)
- \(b = 36\)
- \(c = 39\) (the longest side)
We need to check if:
\[
c^2 = a^2 + b^2
\]
Calculating the squares:
\[
39^2 = 1521
\]
\[
15^2 = 225
\]
\[
36^2 = 1296
\]
Now, adding the squares of the two shorter sides:
\[
15^2 + 36^2 = 225 + 1296 = 1521
\]
Since \(c^2 = a^2 + b^2\) holds true:
\[
39^2 = 15^2 + 36^2
\]
Thus, since \(1521 = 1521\), the triangle is indeed a right triangle.
The correct response is:
**Yes, because 1,521 equals 1,521.**
Here, the sides are:
- \(a = 15\)
- \(b = 36\)
- \(c = 39\) (the longest side)
We need to check if:
\[
c^2 = a^2 + b^2
\]
Calculating the squares:
\[
39^2 = 1521
\]
\[
15^2 = 225
\]
\[
36^2 = 1296
\]
Now, adding the squares of the two shorter sides:
\[
15^2 + 36^2 = 225 + 1296 = 1521
\]
Since \(c^2 = a^2 + b^2\) holds true:
\[
39^2 = 15^2 + 36^2
\]
Thus, since \(1521 = 1521\), the triangle is indeed a right triangle.
The correct response is:
**Yes, because 1,521 equals 1,521.**
Answered by
GPT-4o mini
To determine if a triangle with sides measuring 7, 10, and 12 can be a right triangle, we will apply the Pythagorean theorem. The theorem states that a triangle is a right triangle if the square of the longest side is equal to the sum of the squares of the other two sides.
The sides are:
- \(a = 7\)
- \(b = 10\)
- \(c = 12\) (the longest side)
We need to check if:
\[
c^2 = a^2 + b^2
\]
Calculating the squares:
\[
12^2 = 144
\]
\[
7^2 = 49
\]
\[
10^2 = 100
\]
Now, adding the squares of the two shorter sides:
\[
7^2 + 10^2 = 49 + 100 = 149
\]
Now we compare:
\[
c^2 = 144 \quad \text{and} \quad a^2 + b^2 = 149
\]
Since \(144 \neq 149\), it shows that the Pythagorean theorem does not hold, and thus, the triangle with sides 7, 10, and 12 cannot be a right triangle.
The correct response is:
**No, because 149 does not equal 144.**
The sides are:
- \(a = 7\)
- \(b = 10\)
- \(c = 12\) (the longest side)
We need to check if:
\[
c^2 = a^2 + b^2
\]
Calculating the squares:
\[
12^2 = 144
\]
\[
7^2 = 49
\]
\[
10^2 = 100
\]
Now, adding the squares of the two shorter sides:
\[
7^2 + 10^2 = 49 + 100 = 149
\]
Now we compare:
\[
c^2 = 144 \quad \text{and} \quad a^2 + b^2 = 149
\]
Since \(144 \neq 149\), it shows that the Pythagorean theorem does not hold, and thus, the triangle with sides 7, 10, and 12 cannot be a right triangle.
The correct response is:
**No, because 149 does not equal 144.**
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