Math
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 straightline tunnel from Dubuque to Guatemala City, how long would the tunnel be?

Math 
Anonymous
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 
Math 
Anonymous
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
Respond to this Question
Similar Questions

Physics
Assuming that the Earth is spherical and recalling that latitudes range from 0° at the Equator to 90° N at the North Pole, how far apart, measured on the Earth's surface, are Copenhagen (55.67° N latitude), and Rome (41.90° N latitude)? 
Algebra ii
City B is due north of city A. City A has a latitude of 14.6 degrees N, and city B has a latitude of 47.2 degrees N. find the distance in kilometers between the cities. 
physics
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 … 
physics
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 … 
physics
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 … 
Physics
Assuming that the Earth is spherical and recalling that latitudes range from 0° at the Equator to 90° N at the North Pole, how far apart, measured on the Earth's surface, are Copenhagen (55.67° N latitude), and Rome (41.90° N latitude)? 
Geometry
find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles and that the cities are on the same longitude (one city is due north of the other) Dallas, Texas Latitude: 32* 47' 39" Omaha, Nebraska Latitude: … 
ss
what are latitude and longitude? lines of __________ and lines __________ cross one another. they form a ____________ around the earth. lines of latitude lines of latitude are also called___________ they circle the earth parallel to 
PreCalculus
Two cities are due north of each other. One city has a latitude of 32¢ª45'12" and the second city has a latitude of 51¢ª12'45". Assuming that the earth is a sphere with a radius of 4000 miles, how far apart are the two cities? 
Trig Math
Arc Length Stuff: Have you ever wondered what the circumference of the Earth is?