Anautical 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.

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.

So, 1/60 degrees in radians will be:



Now we can use this value of angle in above equation to find the arc length.

So, rounded of to nearest 10 feet, the length of one nautical mile is 6080 feet.

Yea they are simplyfiy the ratios