Acute / Obtuse Triangles - Math
Card 0 of 772
Two of the exterior angles of a triangle, taken at different vertices, measure 
. Is the triangle acute, right, or obtuse?
Two of the exterior angles of a triangle, taken at different vertices, measure
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At a given vertex, an exterior angle and an interior angle of a triangle form a linear pair, making them supplementary - that is, their measures total 
. The measures of two interior angles can be calculated by subtracting the exterior angle measures from :
The triangle has two interior angles of measure 
.
The measures of the interior angles of a triangle add up to . If 
is the measure of the third angle, then
All three interior angles measure less than 
, making them acute. The triangle is, by definition, acute.
At a given vertex, an exterior angle and an interior angle of a triangle form a linear pair, making them supplementary - that is, their measures total
The triangle has two interior angles of measure
The measures of the interior angles of a triangle add up to
All three interior angles measure less than
Triangle one and triangle two are similar triangles. Triangle one has two sides with lengths 
mm and 
mm. What are possible measurements for the corresponding sides in triangle two?
Triangle one and triangle two are similar triangles. Triangle one has two sides with lengths
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Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.
The ratio of triangle one is:
If we look at the possible solutions we will see that ratio that is in triangle one is also seen in the triangle with side lengths as follows:
Since the two triangles are similar, each triangles three corresponding sides must have the same ratio.
The ratio of triangle one is:
If we look at the possible solutions we will see that ratio that is in triangle one is also seen in the triangle with side lengths as follows:
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{circ}$. The measure of angle CBD is $60^{circ}$. The length of segment $\overline{AD}$ is 4.
Find the measure of angle ADB.
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{circ}$. The measure of angle CBD is $60^{circ}$. The length of segment $\overline{AD}$ is 4.
Find the measure of angle ADB.
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The measure of angle ADB is $30^{circ}$. Since A, B, and C are collinear, and the measure of angle CBD is $60^{circ}$, we know that the measure of angle ABD is $120^{circ}$.
Because the measures of the three angles in a triangle must add up to $180^{circ}$, and two of the angles in triangle ABD are $30^{circ}$ and $120^{circ}$, the third angle, angle ADB, is $30^{circ}$.
The measure of angle ADB is $30^{circ}$. Since A, B, and C are collinear, and the measure of angle CBD is $60^{circ}$, we know that the measure of angle ABD is $120^{circ}$.
Because the measures of the three angles in a triangle must add up to $180^{circ}$, and two of the angles in triangle ABD are $30^{circ}$ and $120^{circ}$, the third angle, angle ADB, is $30^{circ}$.
In ΔABC, A = 75°, a = 13, and b = 6.
Find B (to the nearest tenth).
In ΔABC, A = 75°, a = 13, and b = 6.
Find B (to the nearest tenth).
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This problem requires us to use either the Law of Sines or the Law of Cosines. To figure out which one we should use, let's write down all the information we have in this format:
A = 75° a = 13
B = ? b = 6
C = ? c = ?
Now we can easily see that we have a complete pair, A and a. This tells us that we can use the Law of Sines. (We use the Law of Cosines when we do not have a complete pair).
Law of Sines:
To solve for b, we can use the first two terms which gives us:
This problem requires us to use either the Law of Sines or the Law of Cosines. To figure out which one we should use, let's write down all the information we have in this format:
A = 75° a = 13
B = ? b = 6
C = ? c = ?
Now we can easily see that we have a complete pair, A and a. This tells us that we can use the Law of Sines. (We use the Law of Cosines when we do not have a complete pair).
Law of Sines:
To solve for b, we can use the first two terms which gives us:
The largest angle in an obtuse scalene triangle is 
degrees. The second largest angle in the triangle is 
the measurement of the largest angle. What is the measurement of the smallest angle in the obtuse scalene triangle?
The largest angle in an obtuse scalene triangle is
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Since this is a scalene triangle, all of the interior angles will have different measures. However, it's fundemental to note that in any triangle the sum of the measurements of the three interior angles must equal 
degrees.
The largest angle is equal to 
degrees and second interior angle must equal:
Therefore, the final angle must equal:
Since this is a scalene triangle, all of the interior angles will have different measures. However, it's fundemental to note that in any triangle the sum of the measurements of the three interior angles must equal
The largest angle is equal to
Therefore, the final angle must equal:
In an obtuse isosceles triangle the largest angle is 
degrees. Find the measurement of one of the two equivalent interior angles.
In an obtuse isosceles triangle the largest angle is
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An obtuse isosceles triangle has one obtuse interior angle and two equivalent acute interior angles. Since the sum total of the interior angles of every triangle must equal 
degrees, the solution is:
An obtuse isosceles triangle has one obtuse interior angle and two equivalent acute interior angles. Since the sum total of the interior angles of every triangle must equal
In an acute scalene triangle the measurement of the interior angles range from 
degrees to 
degrees. Find the measurement of the median interior angle.
In an acute scalene triangle the measurement of the interior angles range from
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Acute scalene triangles must have three different acute interior angles--which always have a sum of 
degrees.
Thus, the solution is:
Acute scalene triangles must have three different acute interior angles--which always have a sum of
Thus, the solution is:
The largest angle in an obtuse scalene triangle is 
degrees. The smallest interior angle is 
the measurement of the largest interior angle. Find the measurement of the third interior angle.
The largest angle in an obtuse scalene triangle is
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An obtuse scalene triangle must have one obtuse interior angle and two acute angles.
Therefore the solution is:
All triangles have three interior angles with a sum total of 
degrees.
Thus,
An obtuse scalene triangle must have one obtuse interior angle and two acute angles.
Therefore the solution is:
All triangles have three interior angles with a sum total of
Thus,
The largest angle in an obtuse isosceles triangle is 
degrees. Find the measurement for one of the equivalent acute interior angles.
The largest angle in an obtuse isosceles triangle is
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An obtuse isosceles triangle has one obtuse interior angle and two equivalent acute interior angles. Since the sum total of the interior angles of every triangle must equal 
degrees, the solution is:
An obtuse isosceles triangle has one obtuse interior angle and two equivalent acute interior angles. Since the sum total of the interior angles of every triangle must equal
In an acute isosceles triangle the largest interior angle is 
degrees. Find the measure for one of the two equivalent acute interior angles.
In an acute isosceles triangle the largest interior angle is
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The sum of the three interior angles in any triangle must equal 
degrees. Therefore, the solution is:
The sum of the three interior angles in any triangle must equal
Find the value of 
.
Find the value of
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To find the value of 
, consider the fundamental notion that the sum of the three interior angles of any triangle must equal 
degrees.
Thus, the solution is:
To find the value of
Thus, the solution is:
An obtuse isosceles triangle has an interior angle with a measure of 
degrees.
Select the answer choice that displays the correct measurements for the two other interior angles of the triangle.
An obtuse isosceles triangle has an interior angle with a measure of
Select the answer choice that displays the correct measurements for the two other interior angles of the triangle.
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An obtuse isosceles triangle has one obtuse interior angle and two equivalent acute interior angles. Since the sum total of the interior angles of every triangle must equal degrees, the solution is:
Therefore, each of the two equivalent interior angles must have a measurement of 
degrees each.
An obtuse isosceles triangle has one obtuse interior angle and two equivalent acute interior angles. Since the sum total of the interior angles of every triangle must equal
Therefore, each of the two equivalent interior angles must have a measurement of
A triangle has two equivalent interior angles, each with a measurement of 
degrees. Select the most accurate categorization of this triangle.
A triangle has two equivalent interior angles, each with a measurement of
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The sum of the three interior angles in any triangle must equal degrees. Since this triangle has two equivalent interior angles, it must be an isosceles triangle. Additionally, the sum of the two equivalent interior angles is: 
.
Since, 
degrees, the third interior angle must be a right angle--which makes this triangle an isosceles right triangle.
The sum of the three interior angles in any triangle must equal
Since,
A particular triangle does not have any equivalent sides, and has one interior angle with a measurement of 
degrees.
Select the most accurate categorization of this triangle.
A particular triangle does not have any equivalent sides, and has one interior angle with a measurement of
Select the most accurate categorization of this triangle.
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A scalene triangle doesn't have any equivalent sides or equivalent interior angles. Since this triangle has one obtuse interior angle, it must be an obtuse scalene triangle.
A scalene triangle doesn't have any equivalent sides or equivalent interior angles. Since this triangle has one obtuse interior angle, it must be an obtuse scalene triangle.
A triangle has interior angles that range from 
degrees to 
degrees. What is the most accurate categorization of this triangle?
A triangle has interior angles that range from
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Acute scalene triangles must have three different acute interior angles--which always have a sum of degrees.
Thus, the solution is:
Acute scalene triangles must have three different acute interior angles--which always have a sum of
Thus, the solution is:
A particular triangle has interior angle measurements that range from 
degrees to 
degrees. What is the most accurate categorization of this triangle?
A particular triangle has interior angle measurements that range from
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An obtuse isosceles triangle has one obtuse interior angle and two equivalent acute interior angles. Since the sum total of the interior angles of every triangle must equal degrees, the solution is:
Therefore, this triangle has one interior angle of 
degrees and two equivalent interior angles of 
degrees--making this an obtuse isosceles triangle.
An obtuse isosceles triangle has one obtuse interior angle and two equivalent acute interior angles. Since the sum total of the interior angles of every triangle must equal
Therefore, this triangle has one interior angle of
A triangle has sides of lengths 9, 12, and 18. Is the triangle acute, right, or obtuse?
A triangle has sides of lengths 9, 12, and 18. Is the triangle acute, right, or obtuse?
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Given the lengths of its three sides, a triangle can be identified as acute, right, or obtuse by the following process:
Calculate the sum of the squares of the lengths of the two shortest sides:
Calculate the square of the length of the longest side:
The former is less than the latter. This indicates that the triangle is obtuse.
Given the lengths of its three sides, a triangle can be identified as acute, right, or obtuse by the following process:
Calculate the sum of the squares of the lengths of the two shortest sides:
Calculate the square of the length of the longest side:
The former is less than the latter. This indicates that the triangle is obtuse.
A triangle has sides of lengths 14, 18, and 20. Is the triangle acute, right, or obtuse?
A triangle has sides of lengths 14, 18, and 20. Is the triangle acute, right, or obtuse?
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Given the lengths of its three sides, a triangle can be identified as acute, right, or obtuse by the following process:
Calculate the sum of the squares of the lengths of the two shortest sides:
Calculate the square of the length of the longest side:
The former is greater than the latter. This indicates that the triangle is acute.
Given the lengths of its three sides, a triangle can be identified as acute, right, or obtuse by the following process:
Calculate the sum of the squares of the lengths of the two shortest sides:
Calculate the square of the length of the longest side:
The former is greater than the latter. This indicates that the triangle is acute.
A triangle has sides of lengths 18.4, 18.4, and 26.0. Is the triangle acute, right, or obtuse?
A triangle has sides of lengths 18.4, 18.4, and 26.0. Is the triangle acute, right, or obtuse?
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Given the lengths of its three sides, a triangle can be identified as acute, right, or obtuse by the following process:
Calculate the sum of the squares of the lengths of the two shortest sides:
Calculate the square of the length of the longest side:
The former is greater than the latter. This indicates that the triangle is acute.
Given the lengths of its three sides, a triangle can be identified as acute, right, or obtuse by the following process:
Calculate the sum of the squares of the lengths of the two shortest sides:
Calculate the square of the length of the longest side:
The former is greater than the latter. This indicates that the triangle is acute.
A triangle has sides of lengths 19.5, 46.8, and 50.7. Is the triangle acute, right, or obtuse?
A triangle has sides of lengths 19.5, 46.8, and 50.7. Is the triangle acute, right, or obtuse?
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Given the lengths of its three sides, a triangle can be identified as acute, right, or obtuse by the following process:
Calculate the sum of the squares of the lengths of the two shortest sides:
Calculate the square of the length of the longest side:
The two quantities are equal, so by the Converse of the Pythagorean Theorem, the triangle is right.
Given the lengths of its three sides, a triangle can be identified as acute, right, or obtuse by the following process:
Calculate the sum of the squares of the lengths of the two shortest sides:
Calculate the square of the length of the longest side:
The two quantities are equal, so by the Converse of the Pythagorean Theorem, the triangle is right.