3 City A and City B are approximately a 250 miles apart on

3

City A and City B are approximately a = 250 miles apart on the surface of the earth. Assuming that the radius of the Earth is 4,000 miles, find the radian measure of the central angle with its vertex at the center of the earth that has City A on one side and City B on the other side (see the figure below).

Solution

central angle = arc length/ radius of earth

= 250 miles/4000 miles

= 0.0625 radians

You can round off the answer if required