# Trigonometry and nautical miles

Latitude presents special mathematical considerations for cartographers. Latitude is the north-south location on the earth between the equator and the poles. Since the earth flattens slightly at the poles, a nautical mile varies with latitude. A nautical mile is given by N(e) = 6066 - 31 * cosine 2e. e represents the latitude in degrees.

a) What is the length of a British nautical mile at Chicago (latitude of 42 degrees)?

b) What is the length of a British nautical mile at the North Pole (latitude of 90 degrees)?

Express N(e) in terms of cosine e only, do not use the double angle.

c) At what latitude north is the length of a British nautical mile found to be 6040 feet?

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#### Solution Summary

This shows how to find the length of a British nautical mile at various latitudes using trigonometry.