A circular track has a radius of 15 meters. If a runner covers an arc length of 30 meters, the measure of the central angle in radians that the runner has covered is radians.
Answer & Analysis
Analysis
Question Analysis
This problem assesses the ability to solve for the central angle in radians when given the arc length and the radius.
Key Concept Explanation
The arc length of a circle is given by the formula , where is the radius and is the central angle in radians. To find , rearrange the formula to .
Step-by-step Solution
1. Identify the given values:
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