distance from athens to san francisco

Question

I have a question, how to calculate distance from athens to san francisco?

here is what I did, but it is different than the answer I searched on google

San Francisco & Athena both have 38 degree North Latitude;

San Francisco has 122 degree West Longitude;

Athena has 24 degree East Longitude

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90 degree - 38 degree = 52 degree

sin(52) = opp/hyp= AthensX/R = AthensX/3960

AthensX = 3960Sin(52) = (3960)(.7880) = 3120.522584

122 degree - -24 =degree 146 degree or 2.5481 rad

s = rθ = (3120.522584)(2.5481) = 7951.655447 mile

if don't understand, see the picture below

https://i.stack.imgur.com/hhOXq.png (sorry for my ugly hand writing)

The distance I searched on google is 6783.616 mile

I have no idea about it X~X

Answer 1

First you should go read this answer about the spherical laws of cosines. This will tell you how to compute the "angle" between two points given the latitude and longitude.

Then you multiply the angle, in radians, against the radius of the earth to get the distance in a unit of length.

Another very good explanation is given by our own John Cook on his website.