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A circle has a radius of 13m. Find the radian measure of the central angle theta that intercepts an arc of length 6m. Do not round any intermedlate computations, and round your answer to the nearest tenth.

A circle has a radius of 13 m 13 \mathrm{~m} . Find the radian measure of the central angle θ \theta that intercepts an arc of length 6 m 6 \mathrm{~m} .\newlineDo not round any intermedlate computations, and round your answer to the nearest tenth.

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Full solution

Q. A circle has a radius of 13 m 13 \mathrm{~m} . Find the radian measure of the central angle θ \theta that intercepts an arc of length 6 m 6 \mathrm{~m} .\newlineDo not round any intermedlate computations, and round your answer to the nearest tenth.
  1. Calculate Radian Measure: To find the radian measure of the central angle, we use the formula θ=sr\theta = \frac{s}{r}, where ss is the arc length and rr is the radius.\newlineCalculation: θ=6 m13 m\theta = \frac{6\,\text{m}}{13\,\text{m}}.
  2. Simplify Fraction: Simplify the fraction to get the radian measure.\newlineCalculation: θ=613\theta = \frac{6}{13} radians.
  3. Round to Nearest Tenth: Round the answer to the nearest tenth.\newlineCalculation: θ≈0.5\theta \approx 0.5 radians (rounded to the nearest tenth).

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