SOLUTION: 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 locati
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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.
Assuming the earth is a perfect sphere of radius 4000 miles,what is the distance from the equator to Springfield?
(Approximate to nearest whole number.) Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! draw a line through the center of the circle.
the top of the line is the north pole and the bottom of the line is the south pole.
draw another line through the center of the circle.
each end of the line is at the equator.
the two lines plus the surface of the earth form a plane which is a circle.
half the diameter forms the radius of the circle on either end.
draw another radius that forms an angle of 40.12 degrees with the radius that is at the equator and north of it.
what you have is an arc of the circle.
40 degrees 12 minutes is equal to 40 degrees + 12/60 degrees = 40.2 degrees.
the radius of the circle is 4000 miles.
the circumference is 2 * pi * 4000 = 25,132.74123 miles.
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.
round to the nearest whole number makes it equal to 2806.
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.
the percent error, assuming google is correct, is (2806 - 2739) / 2739 = approximately 2.4% on the high side.
here's a picture of what i explained above.
here's a reference on converting degrees minutes seconds to degrees.
