Final answer:
The length of a 180° arc in a circle with a radius of 9 miles is 9π miles, which is half of the circle's total circumference.
Step-by-step explanation:
The radius of a circle is the distance from the center to any point on the circle, and the arc length is the distance measured along the circumference of the circle that corresponds to a particular angle. In our case, to calculate the length of a 180° arc, we first need the circumference of the circle, which can be found using the formula 2πr (where r is the radius), and then we find the proportion of the circumference that corresponds to a 180° angle, or half a circle.
The circumference of a circle with a radius of 9 miles is given by:
Circumference = 2π × 9 miles = 18π miles.
Since 180° is half of a full 360° rotation, the arc length for 180° will be half of the circumference:
Arc Length for 180° = ½ × 18π miles = 9π miles.