# New york city is located about 40 degrees north of the equator. If Earth's radius is about 4000 miles, approximately how many miles south would a plane need to fly from NYC to reach the equator.

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We are looking for the arc length from NYC to the equator assuming NYC is at `40^@` north latitude and the radius of the earth is 4000 miles.

Draw a sector with central angle `40^@` and radii 4000. Then the arc length is given by `s=40/360(2pi(4000))` (It is a percentage of the circumference of the Earth. What percentage? `40/360=1/9` )

`s=1/9(8000pi)=(8000pi)/9~~2792.5` miles.