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New York and Los Angeles are 2450 mi apart. Find the angle that the arc between
these two cities subtends at the center of earth.(The radius of the earth is 3960 mi.)
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We consider the great circle at the Earth surface, which is the intersection
of the globe sphere with the plane through the center of the sphere and points LA and NY.
As for any circle, the arc length is
S =
where R is the radius of the circle, is the central angle (in radians) and S is the arc length.
For the given problem,
2450 = ,
which gives = = 0.6187 radians = 35.45 degrees.
Solved.