Given triangle with side opposite angle , side opposite angle , and side opposite angle , if , , and , what are the measures of angles and (rounded to the nearest degree)?
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 that line segment is a diameter of circle , what is the measure of the arc subtended by an inscribed angle of ?
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Verified step by step guidance1
Recall the Inscribed Angle Theorem, which states that an inscribed angle in a circle is half the measure of the arc it subtends. Mathematically, if an inscribed angle measures \(\theta\), then the arc it subtends measures \(2\theta\).
Identify the given inscribed angle measure, which is \(56^\circ\) in this problem.
Apply the Inscribed Angle Theorem formula: multiply the inscribed angle by 2 to find the measure of the arc. So, calculate \(2 \times 56^\circ\).
Understand that since \(su\) is a diameter of the circle, the arc subtended by the inscribed angle is not the entire circle but the specific arc opposite the angle, which corresponds to the doubled angle measure.
Conclude that the measure of the arc subtended by the inscribed angle is \(112^\circ\), which is twice the inscribed angle measure.
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