Geometry and TrigonometryHardCentral angle from an arc length
Geometry and Trigonometry practice question
A circle has radius 9. An arc of the circle has length 3π. What is the measure, in degrees, of the central angle that intercepts this arc?
Answer: 60
The full circumference is 2π(9) = 18π. The arc is 3π/18π = 1/6 of the circle, so the central angle is 1/6 of 360° = 60°.
Common wrong answers
- If you answered 3
- 3 is the coefficient of π in the arc length, not the angle. Compare the arc to the whole circumference, 18π.
- If you answered 30
- 30° would correspond to 1/12 of the circle, an arc of 1.5π. The arc here is 1/6 of the circumference.
- If you answered 120
- 120° is 1/3 of the circle, which would need an arc of 6π.
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