distance between two cities

[andreaw]

hello, i am in a trigonometry class which is now online and i have a couple homework problems that involve finding the distance between two cities. my problem is that i was never taught how to do that type of problem and was just told to do the homework. the problem is:

San Fransisco, California 37 degrees, 47 minutes, 36 seconds
Seattle, Washington 47 degrees, 37 minutes, 18 seconds

if someone could help me in figuring out this problem it would be greatly appreciated!

 

[skeeter]

Looks like the problem is assuming the longitude of both cities is very close to being the same, hence the only significant difference is their given latitude.

Recall arclength of a circle, [MATH]s = R\theta[/MATH], where [MATH]\theta[/MATH] is the measure of the central angle in radians and R is the mean radius of the Earth.

for this problem, [MATH]\theta[/MATH] would be the difference between the two latitudes, Seattle Latitude - San Francisco Latitude.
After subtracting, you'll need to convert the deg-min-sec result to radians.

As an aside, navigators know that one minute of arc measured along the same longitude line = one nautical mile.