distances on the earth

To measure the distance between on place or city on the earth to another there is a process of rather simple steps. To do this you must imagine a globe (cirlce) with an equator (dotten line) through the middle. The two places or cities will be given to you in degrees because that is their located of lattitude and longitude on the actual earth. After you do this you must read the problem to determine the next step.

Ex1. Grand Isle,USA is located at 3odegrees N. Lima, Peru is located at 20degrees S. What is the distance between these two cities if the distance of earth is 6024?

A first imagine the globe (you should draw it) with the equator.

B next plot out your two cities. Estimate about 30degrees above your equator for Grand Isle and put a dot. Repeat for the Lima but go 20degrees below because its south. Then draw a dot at the center of the equator. Lastly connect the dots to form a triangel but the two cities should have an arch to represent the earth's curve.

C next you add the two cities degrees to get the central angle. so
30+20=50.
If your two cities are some the same side, such as two north cities or two south, you subtract.

D next you conver to radians by multiplying by pie/180
50*pie/180=5/18pie
you put this is in the center of triangle

F to find the arc length which is your distance use formula S=theta*radius. S=arc length, theta=central arc length, radius is half the diameter of your circle. So to use formula you must find radius. Divide diameter 6024 by 2. So your radius is 3012. Now plug into formula.
S=5/18pie*3012=2628.47
2628.47 miles is the distance.

The End