Arc Length and Nautical Miles

[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!

[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

[Mark44]

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
Wouldn't that be 1.2 miles?

[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.

[Mark44]

That works for me.

[TrueStar]

Thank you both for looking at it!