Given two triangles and , which congruence theorem can be used to prove that they are congruent?
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 sets of numbers could represent the three sides of a triangle according to the Law of Sines ()?
A
, ,
B
, ,
C
, ,
D
, ,
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Verified step by step guidance1
Recall that the Law of Sines states that for a triangle with sides \(a\), \(b\), and \(c\) opposite angles \(A\), \(B\), and \(C\) respectively, the following holds: \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\).
To determine if a set of three numbers can represent the sides of a triangle, first check if they satisfy the triangle inequality: the sum of any two sides must be greater than the third side.
For each set of numbers, verify the triangle inequality: for example, check if \(a + b > c\), \(a + c > b\), and \(b + c > a\).
If the triangle inequality holds, then consider if there exist angles \(A\), \(B\), and \(C\) such that the Law of Sines can be satisfied. This is generally possible if the sides form a valid triangle.
Conclude that the set which satisfies the triangle inequality and can correspond to angles that satisfy the Law of Sines is the valid set of triangle sides.
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