Which equation correctly expresses the Law of Sines for a triangle with sides , , opposite angles , , and ?
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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 equation correctly represents the Law of Sines for a triangle with sides , , opposite angles , , and ?
A
B
C
D
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검증된 단계별 안내1
Recall that the Law of Sines relates the ratios of the lengths of sides of a triangle to the sines of their opposite angles.
Identify the sides and their opposite angles: side \(a\) is opposite angle \(A\), side \(b\) is opposite angle \(B\), and side \(c\) is opposite angle \(C\).
Write the Law of Sines formula as the equality of the ratios of each side length to the sine of its opposite angle: \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\).
Understand that this equation means the ratio \(\frac{\text{side}}{\sin(\text{opposite angle})}\) is constant for all three sides and angles in the triangle.
Compare this with the given options and recognize that the correct representation is the one matching \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\).
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