SOLUTION: 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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Question 1196556: 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.)
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817) About Me  (Show Source):
Answer by ikleyn(52794) About Me  (Show Source):
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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 = R%2Aalpha


where R is the radius of the circle, alpha  is the central angle (in radians) and  S  is the arc length.


For the given problem,

    2450 = 3960%2Aalpha,


which gives  alpha = 2450%2F3960 = 0.6187 radians = 35.45 degrees.

Solved.