In a right triangle, if angle is one of the non-right angles and the other non-right angle measures , what is the 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
2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Multiple Choice
In a right triangle, the radius of a circle is cm and the measure of the central angle is . What is the approximate length of minor arc ? Round to the nearest tenth of a centimeter.
A
cm
B
cm
C
cm
D
cm
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Verified step by step guidance1
Identify the given information: the radius of the circle is 8 cm, and the central angle \( \angle LOM \) measures 60°.
Recall the formula for the length of an arc in a circle: \( \text{Arc length} = r \times \theta \), where \( r \) is the radius and \( \theta \) is the central angle in radians.
Convert the central angle from degrees to radians using the conversion formula: \( \theta_{radians} = \theta_{degrees} \times \frac{\pi}{180} \). For 60°, this becomes \( 60 \times \frac{\pi}{180} \).
Substitute the radius and the angle in radians into the arc length formula: \( \text{Arc length} = 8 \times \left( 60 \times \frac{\pi}{180} \right) \).
Simplify the expression to find the arc length, then round your answer to the nearest tenth of a centimeter.
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