Quadrilateral RSTU is a parallelogram. If angle R measures degrees and angle S measures degrees, what must be the value 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 correctly expresses the Law of Sines for triangle ABC with sides , , opposite angles , , and respectively?
A
B
C
D
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Verified step by step guidance1
Recall that the Law of Sines relates the sides of a triangle to the sines of their opposite angles. For a triangle ABC with sides a, b, and c opposite angles A, B, and C respectively, the Law of Sines states that the ratio of a side length to the sine of its opposite angle is constant for all three sides.
Write the Law of Sines formula as: \(\frac{a}{\sin\left(A\right)} = \frac{b}{\sin\left(B\right)} = \frac{c}{\sin\left(C\right)}\).
Understand that this formula means the ratio of side a to \(\sin(A)\) is equal to the ratio of side b to \(\sin(B)\), and also equal to the ratio of side c to \(\sin(C)\).
Note that other options involving ratios with angles directly (like \(\frac{a}{A}\)) or with cosine functions (like \(\frac{a}{\cos(A)}\)) do not represent the Law of Sines and are incorrect.
Therefore, the correct expression of the Law of Sines is the one that uses the sine of the angles in the denominator, matching the formula \(\frac{a}{\sin\left(A\right)} = \frac{b}{\sin\left(B\right)} = \frac{c}{\sin\left(C\right)}\).
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