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?

Solution Summary

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

At noon, ship A is 30 nauticalmiles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 19 knots. How fast is the distance between the ships changing at 4 PM, in knots? (1 knot is a speed of 1 nautical mile per hour)
- The final result is not around 25 (i.e. 25.XX is not correct). Please check

A nautical mile depends on latitude. It is defined as length of a minute of arc of the earth's radius. The formula is N(P) = 6066 - 31 cos 2P, where P is the latitude in degrees.
a) Find the exact latitude (to 4 decimal places) of where you live, used to live, work, or used to work (include the zip code).
The latitude fo

Two ships are steaming away from a point O along routes that make a 120°angle. Ship A moves at 14 knots (nauticalmiles per hour; a nautical mile is 2000 yards). Ship B moves at 21 knots. How fast are the ships moving apart when OA = 5 and OB = 3 nauticalmiles?

Consider the graph of y = tan x.
(a) How does it show that the tangent of 90 degrees is undefined?
(b) What are other undefined x values?
(c) What is the value of the tangent of angles that are close to 90 degrees (say 89.9 degrees and 90.01 degrees)?
(d) How does the graph show this?
A nautical mile depends on latitud

A ranger in fire tower A spots a fire at a direction of 295 degrees. A ranger in fire tower B, located 45 miles at a direction of 45 degrees from tower A, spots the same fire at direction of 255 degrees. How far from tower A is the fire? From tower B?

1. Consider the graph of y = tan x.
(a) How does it show that the tangent of 90 degrees is undefined?
(b) What are other undefined x values?
(c) What is the value of the tangent of angles that are close to 90 degrees (say 89.9 degrees and 90.01 degrees)?
(d) How does the graph show this?
2. A nautical mile depend

I need some help instructing me how to complete the following questions:
Part 1: From a 220 feet high lighthouse in the Bahamas island of Nassau, a person sees a ship on the horizon. Due to the curvature of earth, how far is the ship from the lighthouse?
Use the formula: d = sqrt[3h/2], where d is the distance in nautical

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

Please see the attached file for the diagram associated with this problem.
Question: An airplane is flying at an altitude of 8 miles towards a point directly over an observer. If the speed of the plane is 615 miles per hour, find the rate at which the angle of observation, theta, changing by at the moment when the angle is 2