Help with distance between cities?

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AI Thread Summary
To find the distance between Panama City and Pittsburgh, the cities' latitudes of 9° N and 40° N are used, assuming they lie on the same north-south line. The formula θ = S/r is relevant, where S is the arc length and r is the radius of the Earth, approximately 6400 km. The latitudes are converted to radians to calculate the arc distance. The distance is determined by solving for S using the difference in latitudes. The discussion concludes with the realization that the calculations can be completed with the provided information.
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Homework Statement


Find the distance in kilometers between each pair of cities assuming they lie on the same north-south line:
Panama City, Panama, 9° N and Pittsburgh, Pennsylvania 40° N

Homework Equations


All we talked about in class is that θ = S/r

The Attempt at a Solution


I'm really not sure what to do... I assume I'm supposed to be solving for s or r, given that θ1 is 9 and θ2 is 40 but...I'm still not sure what to do.
 
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theintarnets said:

Homework Statement


Find the distance in kilometers between each pair of cities assuming they lie on the same north-south line:
Panama City, Panama, 9° N and Pittsburgh, Pennsylvania 40° N


Homework Equations





The Attempt at a Solution


I'm really not sure what to do...

The distance between them is along an arc - if you assume the Earth is a perfect sphere - we commonly do.
 
So what am I supposed to do? All I'm given is 9 and 40. I know I need S or R, but I don't know how to get them.
 
Nevermind, I think I've got it. Apparently the radius of Earth is 6400 km. So I converted the given θ's to radians and then solved for S for the both of them, then subtracted to get the distance between the two :D Thanks for the hint, PeterO
 

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