Which of the following correctly expresses the Law of Sines for triangle ABC with sides , , opposite angles , , and respectively?
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 triangle , which of the following triangles is similar to it?
A
B
C
D
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Verified step by step guidance1
Recall that two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.
Identify the order of vertices in the given triangle \(\triangle jkl\). The order of vertices indicates the correspondence of angles: angle \(j\) corresponds to the first vertex, angle \(k\) to the second, and angle \(l\) to the third.
For each candidate triangle, compare the order of vertices to \(\triangle jkl\) to see if the angles correspond in the same order. For example, in \(\triangle ljk\), the first vertex is \(l\), the second is \(j\), and the third is \(k\).
Check if the angles in the candidate triangle match the angles in \(\triangle jkl\) by matching the vertices in the same order. If the order of vertices corresponds to the same angles, then the triangles are similar.
Conclude that the triangle with vertices ordered to match the angle correspondence of \(\triangle jkl\) is the similar triangle.
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