# Estimate the distance between two cities by its latitude?

Estimate the distance between charleston,South carolina (32°46' N latitude) & Jackson,Wyoming (42°8' N latitude). Btw 3960 is the radius of the earth

- 42°8' - 32°46' = 9°22'

- then 22' / 60 = .36667

- 9.3667 x π/180 = .1635 radians

- .1635 x (3960) = 647.38 miles

My answers book says 741 miles what do i do wrong???

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• Fred
Lv 7
7 years ago

Both you and the answer book are wrong. Not because of any arithmetic errors, per se, but because the question is total nonsense. (Your arithmetic is quite correct, in fact.)

Pope is 100% correct: If you chose two lower-48 US cities at the same (or nearly the same) longitude, then their separation distance would be a simple matter of great-circle arc length, based on their latitude difference.

But if you chose two such cities at the same latitude, but separated by 30º of longitude, this method would give the distance between them as 0, when they would be about 1500 miles apart!

In this instance, the longitudes are nowhere near the same. All this method can do is give a lower limit for the separation distance.

PS: Your arithmetic is correct; as husoski mentions, the latitude for Jackson, WY is off -- from what he gives, I'm guessing you should have had 43º28', not 42º8'. Could've been a simple digit deletion. Then the lat diff becomes 10.7º, and your book's answer looks closer.

Regardless, it is still a misconceived question.

• Pope
Lv 7
7 years ago

The authors of the book want you to use latitude only? That would make a little sense if the cities were near the same longitude, but they are not. In fact, Jackson is more west of Charleston than north. Latitudes alone are not worth much, even for an estimate. You need longitude, or some other information. Perhaps you are expected to do research.

• 7 years ago

Probably one or both of the latitudes is misprinted (or miscopied by you?). When I put in the Google values for latitude for those cities ("coordinates of charleston sc" and "coordinates of jackson wy"), and your radius of the earth, I get 739.0 mi., which is much closer.

Wiki has Jackson at 43.4753N and Charleston at 32.7833N.

• 7 years ago

According to what is given am I correct ? sometimes my teacher put in wrong answers on the key, you think that might be the problem?