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Math Quiz: How Curved Would A Perfectly Flat State of Illinois Be?
Lets assume the State of Illinois is perfectly flat and 400 miles long. Due to the curvature of the Earth, that 400 miles is represented by arc BCD above. r is about 3950 miles. So what is s?
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5.08290992 Miles
Or
4,806.76377 Smoots
1) Circumference (C)= (2*Pi*r) = 24818.581 miles.
2) (400 / C) * 360 = 5.80210425 degrees angle BAD.
3) Draw circle with circumference C in Autocad.
4) Draw two lines BAD degrees apart.
5) Trim arc out of circle using lines.
6) Draw line BD.
7) Dimension S.
8) Post answer, go back to designing measuring machines.
(Measurement results to one part in 100,000 matters to my current employer.
Two jobs ago I was chasing a one part in 1,000,000.
Manufacturing isn't dead in Connecticut quite yet, it just had to move to the fringe to survive.)
Posted by: The Comedian | 05/24/2010 at 07:17 AM
According to the Pythagorean theorem of a2+b2=c2, then s=5.07
BD = 400
r=3950
BD/2 = 200
200 * 200 = 40,000
3950 * 3950 = 15,602,500
So, a2 = 15,562,600
SQRT of 15,562,500 = 3944.93
3950 - 3944.93 = 5.07
Posted by: TooMuchTime | 05/23/2010 at 10:14 PM