Given that ray bisects , and and , what is the measure of ?
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
Which of the following combinations of measurements could form a triangle according to the ?
A
Angle A = , Angle B = , Side a =
B
Angle A = , Angle B = , Side a =
C
Angle A = , Angle B = , Side a =
D
Angle A = , Angle B = , Side a =
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Verified step by step guidance1
First, recall that the Law of Sines states: \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\), where \(a\), \(b\), and \(c\) are sides opposite angles \(A\), \(B\), and \(C\) respectively.
For each given set of measurements, calculate the third angle \(C\) using the triangle angle sum property: \(C = 180^\circ - A - B\).
Check if the third angle \(C\) is positive and less than \(180^\circ\); if not, the measurements cannot form a triangle.
Using the Law of Sines, find side \(b\) corresponding to angle \(B\) by rearranging the formula: \(b = a \times \frac{\sin B}{\sin A}\).
Verify that the calculated side lengths and angles are consistent and possible for a triangle (e.g., all sides positive, angles sum to \(180^\circ\)). The sets that satisfy these conditions could form a triangle.
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