Given triangle , which equation could be used to find the measure of angle using the Law of Sines?
Table of contents
- 0. Review of College Algebra4h 43m
- 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
- OLD 1. Angles and the Trigonometric Functions Coming soon
- OLD 2. Trigonometric Functions graphs, Inverse Trigonometric Functions Coming soon
- OLD 3. Trigonometric Identities and Equations Coming soon
- OLD 4. Laws of Sines, Cosines and Vectors Coming soon
- OLD 5. Complex Numbers, Polar Coordinates and Parametric Equations Coming soon
- NEW (not used) 7. Laws of Sines, Cosines and Vectors Coming soon
- NEW (not used) 8. Vectors Coming soon
- NEW(not used) 9. Polar equations Coming soon
- NEW (not used) 11. Graphing Complex Numbers Coming soon
7. Non-Right Triangles
Law of Sines
Multiple Choice
Given two angle measures and the length of the included side in a triangle, how many distinct triangles can be formed?
A
B
C
D
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Verified step by step guidance1
Identify the given elements: two angles and the included side of a triangle. This corresponds to the ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) case in triangle construction.
Recall the triangle uniqueness theorem for ASA or AAS: if two angles and the included side are known, exactly one unique triangle can be formed because the third angle is determined by the sum of angles in a triangle being 180°.
Calculate the third angle using the formula \(\text{third angle} = 180^\circ - (\text{angle}_1 + \text{angle}_2)\) to confirm the triangle's angle sum property.
Use the Law of Sines or basic geometric construction to verify that the given side length fits uniquely between the two known angles, ensuring only one triangle can be formed.
Conclude that with two angles and the included side given, there is exactly one distinct triangle possible.
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