Honors PreCalculus
posted by Anonymous on .
The latitude of Durham, North Carolina is 36 degrees North. About how far from Durham is the North Pole? Use 3963 miles for the radius of the Earth.
I believe there is a formula of s=r times the feta angle, but you may have to convert the degrees to radians. I'm not sure what I'm doing wrong so if someone could get me going in the right direction I would appreciate it.

I don't know how to figure it using that formula. But each degree of latitude is about 69 miles.

The Earth is not exactly a sphere, but your equation ought to be this:
distance=radiusEarth*theta where theta is the angle in radians. In this case, the angle from the N pole is 9036, or 54 degrees, and converting that to radians 54*PI/180= .942 radians
distance=3963*.942 miles. 
Here's another way of thinking about it. You know the Radius, 3963 so you can now find the circumference with the formula C=2piR. Do the math, C=24900. Durham is at 36 degrees which means Durham to the north pole is 54 degrees. Draw a little picture. The ratio of 54/360 degrees will give you the percentage of the earth from Durham to the north pole. So, multiply that ratio times the total circmference to get the distance.
54/360*24900=3735 miles. This is probably not the way your teacher wants you to do this problem but it works