Variation of distance scales across the earth
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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.
What is the length of a British nautical mile at Chicago (latitude of 42 degrees)?
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.
At what latitude north is the length of a British nautical mile found to be 6040 feet?
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A) What is the length of a British nautical mile at Chicago (latitude of 42 degrees)?
We have the relation N(e) = 6066 - 31 * cosine 2e
with e = 42, it becomes,
N(42) = 6066 - 31 cos 2(42)
= 6066 - 31 cos 84
= ...
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