Math
posted by rachel on .
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 straightline tunnel from Dubuque to Guatemala City, how long would the tunnel be?

42.50  14.62 = 27.88 °
The circumference of a circle = 2 r pi
The formula for the arc length of a circle:
L = 2 r pi * theta / 360 ° = r pi * theta / 180 °
The average radius of the Earth is 6371 km
L = 6371 * pi * 27.88 ° / 180 ° = 3100.115 km
Approx. 3100 km 
L = The length of that arc between Dubuque and Guatemala City
The length of the tunnel = The chord length :
c = 2 r sin ( theta / 2 )
c = 2 * 6371 * sin ( 27.88 ° / 2 )
c = 2 * 6371 * sin 13.94 °
c = 2 * 6371 * 0.24091
c = 3069.67522 km
Approx. 3070 km