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Homework Help: Arc Length and Nautical Miles

  1. Aug 28, 2009 #1
    1. The problem statement, all variables and given/known data

    Given: The diameter of the Earth is 8000 miles

    If angle ACB has measure 1', then the distance between A and B is a nautical mile. Approximate the number of and (statute) miles in a nautical mile.

    2. Relevant equations

    Arc Length Therom: s=r(theta)

    3. The attempt at a solution

    I think I have this figured out and I was just over-thinking it, but I'd like to check with others.

    1'=1/60 degrees, but this needs to be changed to radians so it can be used in the arc length formula. --- 1/60*pi/180 = pi/10800 radians.

    Apply this along with the Earth's radius (8000/2 = 4000 miles) to the arc length formula --- (pi/10800)*4000 = 4000pi/10800 miles. This simplifies out to10pi/27 or about 1.16 miles per nautical mile. However, I will put down 10pi/27 because my instructor wants exact answers.

    Did I do this correcty? Thanks in advance!
  2. jcsd
  3. Aug 28, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    In a circle there are 360 x 60 minutes of arc.
    1' at the equator is a nautical mile.
    The equator is pi*8000 statute miles

    Since you are only given the Earth's diamter to 1 sig figure then 1.6mi would be an exact answer
  4. Aug 28, 2009 #3


    Staff: Mentor

    Wouldn't that be 1.2 miles?
  5. Aug 28, 2009 #4
    Maybe I'm using the wrong wording. He wants everything to have pi remain in the answer if pi is part of it. He doesn't want us to plug it into a calculator and submit answers in decimal form.

    This is why I say I think the answer is 10pi/27.
  6. Aug 28, 2009 #5


    Staff: Mentor

    That works for me.
  7. Aug 28, 2009 #6
    Thank you both for looking at it!
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