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

Algebra ->  Trigonometry-basics -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
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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   %2864.3%2F360%29%2A2pi%2AR = %2864.3%2F360%29%2A2%2A3.14159%2A3960 = 4444  miles     (rounded).         ANSWER

Solved and carefully explained.