posted by rachel .
Assume that the Earth is spherical and recall that latitudes range from 0° at the Equator to 90° N at the North Pole. Consider Dubuque, Iowa (42.50° N latitude), and Guatemala City (14.62° N latitude). The two cities lie on approximately the same longitude. Do not neglect the curvature of the Earth in determining the following.
If one could burrow through the Earth and dig a straight-line tunnel from Dubuque to Guatemala City, how long would the tunnel be?
The subtended angle between the two cities, measured from the Earth's center, is 42.50-14.62 = 27.88 degrees
(You can take the difference of the two latitudes since the longitudes are the same.)
The distance you want is the base of an isosceles triangle with two equal sides R (the earth radius) and apex angle A = 27.88 degrees.
R = 6370 km
Tunnel Length = 2*R*sin(A/2)= 3069 km