SOLUTION: Hello there, I just need help figuring this out, I put down 657 mi but apparently I did something wrong cause it was incorrect. Assume the Earth is approximately spherical with

Question 1182019: Hello there, I just need help figuring this out, I put down 657 mi but apparently I did something wrong cause it was incorrect.
Assume the Earth is approximately spherical with radius 3960mi. Approximate the distance to the nearest mile.
City A (36.9∘N,150.1∘W) is located north of the equator, and City B (27.4∘S,150.1∘W) is located south of the equator. The longitudes are the same indicating that the cities are due north-south of each other. Use the difference in latitudes to approximate the distance between the cities.
Answer by ikleyn(52915)   (Show Source): You can put this solution on YOUR website!
.

Since the longitude is the same, the points A and B lie in one great circle of the Earth globe,

which (the great circle) also goes through the poles.

So the distance between the points A and B on the Earth globe is the length of the arc of the great circle.

The degree measure of the arc is 36.9 degrees   PLUS   27.4 degrees = 64.3 degrees.

            I write PLUS because the points are in different hemi-spheres ( ! )

So the distance on the globe surface is    = = 4444 miles     (rounded).         ANSWER

Solved and carefully explained.

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