document.write( "Question 1164109: Latitude gives the measure of a central angle θ with vertex at the earth's center whose initial side goes through the equator and whose terminal side goes through the given location.The latitude of Springfield, Illinois is 40°12′ north.
\n" ); document.write( "Assuming the earth is a perfect sphere of radius 4000 miles,what is the distance from the equator to Springfield?
\n" ); document.write( "(Approximate to nearest whole number.) \n" ); document.write( "
Algebra.Com's Answer #788497 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
draw a line through the center of the circle.
\n" ); document.write( "the top of the line is the north pole and the bottom of the line is the south pole.
\n" ); document.write( "draw another line through the center of the circle.
\n" ); document.write( "each end of the line is at the equator.
\n" ); document.write( "the two lines plus the surface of the earth form a plane which is a circle.
\n" ); document.write( "half the diameter forms the radius of the circle on either end.
\n" ); document.write( "draw another radius that forms an angle of 40.12 degrees with the radius that is at the equator and north of it.
\n" ); document.write( "what you have is an arc of the circle.
\n" ); document.write( "40 degrees 12 minutes is equal to 40 degrees + 12/60 degrees = 40.2 degrees.
\n" ); document.write( "the radius of the circle is 4000 miles.
\n" ); document.write( "the circumference is 2 * pi * 4000 = 25,132.74123 miles.
\n" ); document.write( "the length of the arc is equal to 40.2 / 360 * 2 * pi * r = 40.2 / 360 * 25,132.74123 = 2806.489437 miles from the equator.
\n" ); document.write( "round to the nearest whole number makes it equal to 2806.
\n" ); document.write( "google says the distance from springfield, illinois to the equator is 2739 miles, so the answer is a little high, but not too far off.
\n" ); document.write( "the percent error, assuming google is correct, is (2806 - 2739) / 2739 = approximately 2.4% on the high side.
\n" ); document.write( "here's a picture of what i explained above.\r
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\n" ); document.write( "\n" ); document.write( "here's a reference on converting degrees minutes seconds to degrees.\r
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\n" ); document.write( "\n" ); document.write( "https://www.rapidtables.com/convert/number/degrees-minutes-seconds-to-degrees.html\r
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