Which of the following lists of angle measures could be the angle measures of a triangle?
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
7. Non-Right Triangles
Law of Sines
Multiple Choice
Which of the following sets of angles can be used to construct a triangle?
A
, ,
B
, ,
C
, ,
D
, ,
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Verified step by step guidance1
Recall the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle must be exactly \(180^\circ\).
For each set of angles, add the three angles together using the formula: \(\text{Sum} = \alpha + \beta + \gamma\), where \(\alpha\), \(\beta\), and \(\gamma\) are the angles in degrees.
Check if the sum of the angles in each set equals \(180^\circ\). If the sum is exactly \(180^\circ\), then the set of angles can form a triangle.
Verify that each individual angle is greater than \(0^\circ\) because angles must be positive to form a valid triangle.
Conclude which sets satisfy both conditions: sum equals \(180^\circ\) and all angles are positive, indicating those sets can be used to construct a triangle.
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