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# distance between cities?

Memphis,Tennesee is due north of New Orleans, Louisiana. Find distance between Memphis(35 degrees 9' north latitude) and New Orleans ( 29 degrees 57' north latitude). Assume that the radius of Earth is 3960 miles.

plz & thank you

okay and iv gotten alot of answers...but non explain how hey get the distance to be 5 degrees 12minutes, so please explain ,thanx

### 3 Answers

- 1 decade agoFavorite Answer
Both minutes and seconds are in 60ths. So Memphis is at 35 and 9/60 degrees, while N.O. is at 29 and 57/60 degrees.

If you assume that the radius of the Earth is 3960 miles, you can assume that the distance from the center of the Earth to both cities is the same 3960 miles (approximately). When you subtract the two latitude measurements, you find the distance between the locations.

This makes 5 and 12/60 degrees (don't simplify the fractions).

If you are using a calculator, you will get 5.2. Take the integer and it is the degree measurement. Take the decimal part and multiply it by 60 - that's your minutes measurement. Take any remaining decimal, multiply it by 60 and that's your seconds measurement. Leave decimals attached to seconds.

If you want the distance in miles (I'm assuming) you need to find the arc-length using a proportion:

degree difference / degrees around the Earth = miles difference / miles around the Earth

Notice that you can only find the distance between the cities after finding the circumference of the Earth.

5.2 / 360 = x / (pi*2*3960)

Multiply both sides by the lower portion of the right side to get x by itself:

5.2*pi*7920 / 360 = x = (about) 359.40 miles

You'll definitely want to check that; MS Calculator is only as good as the user...

- 1 decade ago
OK, you need to get how far 1 degree on the earth's surface in terms of miles. In other words, you need the circumference of the earth divided by 360 degrees.

Circumference of earth is 2 * PI * R

I get 24881 miles.

So each degree is 69.11 miles

Now we have to convert 5 degrees and 12 minutes to a decimal.

(12 / 60) + 5 = 5.2

Now. after multiplying these we get the final distance of 359.2 miles (www.maps.google.com says a road distance of 395 miles so ~360 sounds reasonable).