Given triangle where and are on straight lines and respectively, and the measure of angle is and angle is , what is the measure of angle (angle ) in degrees?
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 equation could be used to find the measure of angle using the Law of Sines?
A
B
C
D
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Verified step by step guidance1
Recall the Law of Sines, which states that in any triangle, the ratio of the sine of an angle to the length of the side opposite that angle is constant. Mathematically, this is expressed as: \(\frac{\sin(\angle A)}{a} = \frac{\sin(\angle B)}{b} = \frac{\sin(\angle C)}{c}\), where \(a\), \(b\), and \(c\) are the sides opposite angles \(A\), \(B\), and \(C\) respectively.
Identify the vertices and sides of triangle \(\triangle efg\). The angle \(e\) is opposite side \(fg\), angle \(f\) is opposite side \(eg\), and angle \(g\) is opposite side \(ef\).
Set up the Law of Sines ratio involving angle \(e\) and its opposite side \(fg\), and angle \(f\) and its opposite side \(eg\). This gives the equation: \(\frac{\sin(e)}{fg} = \frac{\sin(f)}{eg}\).
Note that this equation allows you to solve for \(\sin(e)\) or the measure of angle \(e\) if the lengths of sides \(fg\) and \(eg\) and the measure of angle \(f\) are known.
Confirm that this matches the correct choice among the given options, which uses the Law of Sines correctly by pairing each angle with its opposite side.
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