Find the length of the arc if the central angle is 3 degrees and the radius is 4,000 miles
To find the length of the arc, we need to use the formula:
Arc length = (central angle/360) * 2 * π * radius
Given that the central angle is 3 degrees and the radius is 4,000 miles, the formula becomes:
Arc length = (3/360) * 2 * π * 4000
Simplifying further:
Arc length = (1/120) * 2 * π * 4000
Arc length = (1/60) * π * 4000
Arc length = (π/60) * 4000
Using the approximation π ≈ 3.14, we get:
Arc length ≈ (3.14/60) * 4000
Arc length ≈ 209.33 miles
Therefore, the length of the arc is approximately 209.33 miles.