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Q: Given two points on the globe, how do you figure out the direction and distance to each other?
Physicist: The very short answer is: use the spherical law of cosines so you can do trigonometry on a sphere. As you may have heard, the shortest distance between two points is a straight line. For curved surfaces the closest you can get to a straight line is a “geodesic”, which is a straight line on small scales, but it you step back may be going all over the place. If you walk in a straight line, you’re walking on a great circle. The law of cosines (either of them) relates four things: all three sides and one of the angles.
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