a circle has a radius of 3. an arc in this circle has a central angle of $20^{\\circ}$.\n\nwhat is the…

a circle has a radius of 3. an arc in this circle has a central angle of $20^{\\circ}$.\n\nwhat is the length of the arc?\neither enter an exact answer in terms of $\\pi$ or use 3.14 for $\\pi$ and enter your answer as a decimal.

a circle has a radius of 3. an arc in this circle has a central angle of $20^{\\circ}$.\n\nwhat is the length of the arc?\neither enter an exact answer in terms of $\\pi$ or use 3.14 for $\\pi$ and enter your answer as a decimal.

Answer

Explanation:

Step1: Identify the arc length formula

$$s = \frac{\theta}{360^{\circ}} \times 2\pi r$$

Step2: Substitute the given values

$$s = \frac{20^{\circ}}{360^{\circ}} \times 2\pi(3)$$

Step3: Simplify the fraction and multiply

$$s = \frac{1}{18} \times 6\pi$$

Step4: Calculate the exact value

$$s = \frac{\pi}{3}$$

Step5: Calculate the decimal value using 3.14

$$s \approx \frac{3.14}{3} \approx 1.0466...$$

Answer:

\frac{\pi}{3} or 1.0466...