A circle has a radius of inches and a central angle of . What is the approximate length of the arc subtended by this angle? Choose the closest value.
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
2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Multiple Choice
Given that the measure of arc ED is , what is the measure of angle EFD if angle EFD is an inscribed angle that intercepts arc ED?
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Verified step by step guidance1
Recall the definition of an inscribed angle: an inscribed angle is an angle formed by two chords in a circle which have a common endpoint. The vertex of the angle lies on the circle, and the angle intercepts an arc.
Understand the key property of inscribed angles: the measure of an inscribed angle is exactly half the measure of the intercepted arc.
Identify the given information: the measure of arc ED is \(68^\circ\), and angle EFD is an inscribed angle intercepting this arc.
Apply the inscribed angle theorem formula: if \(\angle EFD\) intercepts arc \(ED\), then \(\angle EFD = \frac{1}{2} \times \text{measure of arc } ED\).
Substitute the given arc measure into the formula: \(\angle EFD = \frac{1}{2} \times 68^\circ\) to find the measure of angle EFD.
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