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Find the arc length along a circle of radius 10 units subtended by an angle of 260°. Round your answer to the nearest tenth. Provide your answer below: units

Find the arc length along a circle of radius 10 units subtended by an angle of 260°. Round your answer to the nearest tenth. Provide your answer below: units

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** Find the arc length along a circle of radius 10 units subtended by an angle of 260°. Round your answer to the nearest tenth. **Solution:** To find the arc length \(L\) of a circle, the formula is: \[ L = \frac{\theta}{360^\circ} \times 2\pi r \] where: - \( \theta \) is the central angle in degrees. - \( r \) is the radius of the circle. For this problem: - \( \theta = 260^\circ \) - \( r = 10 \) units Plug these values into the formula: \[ L = \frac{260}{360} \times 2\pi \times 10 \] Calculate the arc length and round to the nearest tenth: 1. Simplify \(\frac{260}{360}\) to get \(\frac{13}{18}\). 2. Compute \( L = \frac{13}{18} \times 20\pi \). 3. Approximate \(\pi \approx 3.1416\). 4. Calculate \(L \approx \frac{13}{18} \times 62.832\). 5. Final answer: \(L \approx 45.4\) units. **Answer:** The arc length is approximately 45.4 units.
Transcribed Image Text:**Problem Statement:** Find the arc length along a circle of radius 10 units subtended by an angle of 260°. Round your answer to the nearest tenth. **Solution:** To find the arc length \(L\) of a circle, the formula is: \[ L = \frac{\theta}{360^\circ} \times 2\pi r \] where: - \( \theta \) is the central angle in degrees. - \( r \) is the radius of the circle. For this problem: - \( \theta = 260^\circ \) - \( r = 10 \) units Plug these values into the formula: \[ L = \frac{260}{360} \times 2\pi \times 10 \] Calculate the arc length and round to the nearest tenth: 1. Simplify \(\frac{260}{360}\) to get \(\frac{13}{18}\). 2. Compute \( L = \frac{13}{18} \times 20\pi \). 3. Approximate \(\pi \approx 3.1416\). 4. Calculate \(L \approx \frac{13}{18} \times 62.832\). 5. Final answer: \(L \approx 45.4\) units. **Answer:** The arc length is approximately 45.4 units.
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