Given that , , , and , which of the following best describes the relationship between the angles in two triangles that allows the Law of Sines to be applied?
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- 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 correctly states the Law of Sines for a triangle with sides , , opposite angles , , , specifically relating a single pair of side and opposite angle?
A
B
C
D
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Verified step by step guidance1
Recall that the Law of Sines relates the ratios of the lengths of sides of a triangle to the sines of their opposite angles.
For a triangle with sides \(a\), \(b\), and \(c\) opposite angles \(A\), \(B\), and \(C\) respectively, the Law of Sines states that the ratio \(\frac{a}{\sin A}\) is equal to \(\frac{b}{\sin B}\) and also equal to \(\frac{c}{\sin C}\).
This means the full Law of Sines can be written as:
\(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\)
If the problem asks specifically for the relationship involving a single pair of side and opposite angle, then the correct expression is:
\(\frac{a}{\sin A} = \frac{b}{\sin B}\)
Note that expressions involving ratios of sides to angles directly (like \(\frac{a}{A}\)) or involving cosine instead of sine do not represent the Law of Sines.
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