Pre calculus 4.1

Question

If angle ACB is 25 degrees and line AC is 4000 miles (the radius of the earth). Find the distance between points A and B.

Answer 1

Sounds like points A and B are on the surface of the Earth, along a great circle having the center of Earth as its center. The arc length AB is in the same proportion to the circumference of this circle as 25° is to 360°: AB/(2πR) = 25/360, AB = 0.069444 (2π*4000) = 1745 miles.