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November 20th, 2007, 01:23 PM   #1
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Finding the distance between two points on a sphere

I can't figure the following question out and need to know how it's done:

Find the distance between the two cities. Assume the Earth is a sphere of radius 4000 miles and that the cities are on the same meridian. (one city is due north of the other)

Dallas -- 32° 47' 9" N

Omaha -- 41° 15' 42"N

Thanks for any help given.
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November 20th, 2007, 01:30 PM   #2
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So you have the two cities on a circle, with the arc connecting them being 8.5 or so degrees. So given the radius you can find the circumference, right? Then find the appropriate fraction of that circumference, given that there are 360 degrees in total.
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November 20th, 2007, 01:37 PM   #3
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Quote:
Originally Posted by CRGreathouse
So you have the two cities on a circle, with the arc connecting them being 8.5 or so degrees. So given the radius you can find the circumference, right? Then find the appropriate fraction of that circumference, given that there are 360 degrees in total.
Thanks, that was very helpful. I have it now.
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November 20th, 2007, 02:24 PM   #4
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Quote:
Originally Posted by jokerthief
Thanks, that was very helpful. I have it now.
Actually I appreciated the problem. I find geometry intimidating, and I enjoyed an opportunity to solve a problem in it, if only a simple one.
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November 7th, 2018, 11:10 PM   #5
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41° 15' 42" - 32° 47' 9" = 8° 28' 33" = 8.4758333° approximately.

Hence required distance is 2ππ × 4000 miles × 8.475833333 / 360 = 591.7248 miles approximately.

This assumes that the distance is measured along the meridian.
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