A nautical mile is a unit of distance frequently used in ocean navigation. It is defined as the length of an arc s along a great circle on the earth when the subtending angle has measure 1' = "one minute" = 1/60 of one degree. Assume the radius of the earth is 3,960 miles.Find the length of one nautical mile to the nearest 10 feet.
Accepted Solution
A:
The length of an arc can be related to the radius of circle and the angle it makes at the center of the circle by following equation:
s = rФ
Radius is given to be = 3960 miles We are to find the arc length in feet, so we convert the miles to feet. 1 mile = 5280 feet. So, Radius = 3960 x 5280 feet = 20908800 feet Angle = 1/60 degree The angle must be in radians before, we use its value in the equation given above.