Answer :
Final answer:
The length of the arc subtended by a 66° central angle in a circle with a radius of 15 miles is approximately 17.28 miles. This is found using the arc length formula s = rθ, where r is the radius and θ is the angle in radians.
Explanation:
To find the length s of the arc of a circle, you can use the formula s = rθ, where r is the radius of the circle and θ is the central angle in radians. To convert degrees to radians, we use the ratio 180 degrees = π radians. Therefore, to find the arc length for a circle of radius 15 miles with a central angle of 66 degrees, you would perform the following steps:
- Convert 66 degrees to radians by multiplying by π/180. This gives us 66 * π/180 = 1.15 radians.
- Then, plug the values into the arc length formula: s = rθ = 15 miles * 1.15 radians = 17.28 miles.
- O>
So, the length of the arc subtended by a 66° central angle in a circle with a radius of 15 miles is approximately 17.28 miles.
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