Distance between Two Cities on Earth

[Mathlete]

Hey guys, I have been having trouble with this problem.

I can get the answer fairly easily using the approximation of 1 degree = 69 miles latitude, 80 degrees * 69 degrees/mile = 5520 miles apart, but I cannot get the 5529 that the answer choice states using normal methods.

My attempt:

I get the answer that is closest to D, but I cannot get the exact answer and I cannot find where I made this mistake. Any help would be appreciated.

Thank you.

 

[DrPhil]

View attachment 2713
Hey guys, I have been having trouble with this problem.

I can get the answer fairly easily using the approximation of 1 degree = 69 miles latitude, 80 degrees * 69 degrees/mile = 5520 miles apart, but I cannot get the 5529 that the answer choice states using normal methods.

My attempt:
View attachment 2714
I get the answer that is closest to D, but I cannot get the exact answer and I cannot find where I made this mistake. Any help would be appreciated.

Thank you.

You need to scale using the numbers given in the problem, NOT some other approximation of the miles per arc-minute. Instead, convert the latitude difference to radians, and then the definition angle in radians = arc length / radius.

EDIT: They want the distance measured along the surface of the Earth - how far do you have to go to get there!!

 

[Mathlete]

Thank you!

Yes, along the surface of the earth, which turned out to be easier to calculate than the direct distance, the answer was 5529.2, which is what it was supposed to be.

Once again, thanks!