A circular track has a radius of 20 units. If a runner covers an arc length of 30 units, the central angle in radians that the runner has covered is radians.
Answer & Analysis
Analysis
Question Analysis
This problem assesses the ability to find the central angle in radians given the arc length and the radius of a circle.
Key Concept Explanation
The formula for the arc length of a circle with radius and central angle (in radians) is given by . To find the central angle, rearrange the formula to solve for : .
Step-by-step Solution
1. Use the arc length formula
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