SOLUTION: If the latitude of Chicago is about 42 degrees and the radius of the earth is about 4000 miles, how far is Chicago from the equator? (using pi=3.1416)

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Question 253723: If the latitude of Chicago is about 42 degrees and the radius of the earth is about 4000 miles, how far is Chicago from the equator? (using pi=3.1416)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
If you take a vertical cross section of the earth through chicago, you have a circle.

The center of the earth is the center of the circle.

The angle formed from the center of the circle to chicago, and from the center of the circle to the equator is equal to 42 degrees.

The surface of that circle is the circumference of the earth.

the radius of the circle is 4000 miles.

the circumference of the circle is equal to 2 * pi * 4000 = 8000 * pi = 8000 * 3.1416 = 25132.8 miles.

The distance from chicago to the equator is equal to 42/360 * 25132.8 miles = 2932.16 miles.

I checked with a distance calculator from the surface of the earth and got 2869 miles.

That calculator shows the latitude of chicago to be 41.49 degrees north.

I replaced 41.49N with 42N and got 2904 miles.

That's even closer so I'm pretty confident that I did it right.

That calculator can be found at the following link.

http://www.wfu.edu/biology/albatross/gcircle/calcfull.html

this problem assumes the earth is perfectly round which it is not so real world calculations will be different after taking that into account.