Edward C. answered • 07/30/15

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If you model the Earth as a sphere with radius R then the circumference of the circle at the equator is 2*pi*R. A "line of constant latitude" will form a circle with a smaller radius - think of slicing the sphere across at the given latitude. If you draw a picture you will see that the radius of the circle along a line of constant latitude is R*cos(LAT). So the circumference of the circle along a line of constant latitude is 2*pi*R*cos(LAT). The two cities are separated by

(141 degrees 2') - (52 degrees 5') = (88 degrees 57') = 88.95 degrees so the length of the arc between them is

(88.95 / 360) of the full circle. If you use R = 3959 miles you will get

D = 2*pi*3959*cos(38.783)*(88.95/360) = 4791 = 4.79*10^3 miles

Jason W.

07/31/15