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 November 20th, 2007, 12:23 PM #1 Member   Joined: Oct 2007 Posts: 31 Thanks: 0 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. November 20th, 2007, 12:30 PM #2 Global Moderator   Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 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. November 20th, 2007, 12:37 PM   #3
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 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. November 20th, 2007, 01:24 PM   #4
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 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. November 7th, 2018, 10:10 PM #5 Global Moderator   Joined: Dec 2006 Posts: 20,757 Thanks: 2138 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. Tags distance, finding, points, sphere ,

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find the distance between the cities. assume that earth is a sphere of radius 4000 miles and that the cities are on the same longitude (one city is due north of the other). (round your answer to one decimal place.)

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