In a right triangle, one leg measures units and the other leg measures units. Find the measure of the angle opposite the side of length to the nearest degree.
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
In a circle, the length of an arc intercepted by a central angle is . If the radius of the circle is , what is the measure of the central angle in radians?
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Verified step by step guidance1
Recall the formula that relates the arc length \(s\), the radius \(r\), and the central angle \(\theta\) in radians:
\(s = r \times \theta\)
Identify the given values from the problem: the arc length \(s = 12\) mm and the radius \(r = 8\) mm.
Substitute the known values into the formula:
\(12 = 8 \times \theta\)
Solve for the central angle \(\theta\) by dividing both sides of the equation by 8:
\(\theta = \frac{12}{8}\)
Simplify the fraction \(\frac{12}{8}\) to its lowest terms to find the measure of the central angle in radians.
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