The distance between two points A and B on Earth is measured along a circle having center C at the center of Earth and radius equal to the

Question

distance from C to the surface (see the figure). Assume the diameter of Earth is approximately 8,000 miles. If angle ACB has measure 1', then the distance between A and B is a nautical mile. Approximate the number of land (statute) miles in a nautical mile.

Answer 1

The circumference of the Earth, a circle, is 2 π R, so we can find the circumference of the Earth = 2 π 4,000 miles.

 

A minute of arc is 1/60th of a degree.  A degree is 1/360th of a circle.  So the number of miles in a minute of arc is:

Distance / [60 x 360].  Use this to find the number of miles in a minute of arc.  This you can compare this to the "nautical mile" that is defined to be this distance!