Given a right triangle where angle is one of the non-right angles and the side opposite angle is units while the side adjacent to angle is units, which is the approximate measure of angle ?
Table of contents
- 0. Review of College Algebra4h 45m
- 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
1. Measuring Angles
Angles in Standard Position
Multiple Choice
Segments and are diameters of circle . What is the measure of the angle formed by these diameters if the angle is greater than and less than ?
A
B
C
D
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Verified step by step guidance1
Understand that segments AC and BD are diameters of circle O, meaning both pass through the center O and each subtends a straight angle of 180° at the center.
Identify that the angle formed by these two diameters at the center O can be measured as the smaller angle between the two lines or the larger reflex angle, which is between 180° and 360°.
Note that the problem asks for the angle measure greater than 180° and less than 360°, so we are looking for the reflex angle between the two diameters.
If the smaller angle between the diameters is given or can be found (for example, 107°), calculate the reflex angle by subtracting this smaller angle from 360° using the formula: \(360^\circ - \text{smaller angle}\).
Apply this formula to find the reflex angle formed by the diameters, which will be the angle measure between 180° and 360° as required.
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