Question

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?

-->I know the answer for above and it is
3072992.8 m..i need help with part b


b)From the point of view of the digger, at what angle below the horizontal would the tunnel be directed?

Answer 1

If the tunnel length is L and the Earth radius is R, the angle below horizontal is
arcsin [L/(2R)]

Prove it to yourself by drawing a circular arc and a straight line between the two cities, with the center of the Earth as the center of the arc. A line from the center of the Earth to the center of the straight line (tunnel) forms a right triangle with hypotenuse R, angle A at the Earth center, and one side equal to L/2.

A = arcsin [L/(2R)]

Look up R. It is about 6.4*10^6 m
I get about 29 degrees. .

Answer 2

for L, are you using the answer from part a?? when i use that i get around 14 degrees