SOLUTION: 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 flatte

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Question 40736: 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?

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+N%28e%29+=+6066+-+31%2Acos%282e%29+

Chicago (42degrees):
+N%28e%29+=+6066+-+31cos%282e%29+
+N%28e%29+=+6066+-+31cos%282%2A42%29+
+N%28e%29+=+6066+-+31cos%2884%29+
N(e) = 6062.76 feet

North Pole (90 degrees):
+N%28e%29+=+6066+-+31cos%282e%29+
+N%28e%29+=+6066+-+31cos%282%2A90%29+
+N%28e%29+=+6066+-+31cos%28180%29+
+N%28e%29+=+6066+%2B+31+
N(e) = 6097 feet

TRIG IDENTITY:
+cos%282e%29+=+2cos%5E2%28e%29+-+1+ so we then get:

+N%28e%29+=+6066+-+31%282cos%5E2%28e%29+-+1%29+
+N%28e%29+=+6066+-+62cos%5E2%28e%29+%2B+31+
+N%28e%29+=+6097+-+62cos%5E2%28e%29+

When nautical mile = 6040feet:
+N%28e%29+=+6066+-+31cos%282e%29+
+6040+=+6066+-+31cos%282e%29+
+-26+=+-+31cos%282e%29+
+%28-26%29%2F%28-31%29+=+cos%282e%29+
+%2826%29%2F%2831%29+=+cos%282e%29+
+2e+=+cos%5E%28-1%29%28%2826%29%2F%2831%29%29+
2e = 33 degrees to 2significant places
--> e = 33/2
--> e = 16.5 degrees latitide

jon.