# Homework Help: Arc Length and Nautical Miles

1. Aug 28, 2009

### TrueStar

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. Aug 28, 2009

### mgb_phys

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

3. Aug 28, 2009

### Staff: Mentor

Wouldn't that be 1.2 miles?

4. Aug 28, 2009

### TrueStar

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.

5. Aug 28, 2009

### Staff: Mentor

That works for me.

6. Aug 28, 2009

### TrueStar

Thank you both for looking at it!