Trigonometry and nautical miles
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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.
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.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
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- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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