Honors PreCalculus
posted by Anonymous .
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
Respond to this Question
Similar Questions

physical geography
If you begin at 20 degrees 47'36" south and 168 degrees 23'46" west, and go 50 degrees north and 50 degrees west of there, where would you be? 
GEOGRAPHY
How many degrees is the Arctic Circle displaced from the North Pole? 
Science
If you were flying directly south from the north pole and reached 70 degrees north latitude, how many more degrees of latitude would be left to pass over before you reached the south pole? 
Trigonometry
Smalltown, latitude 53.6 degrees N, lies directly north of Bigville, latitude 38.6 degrees N. Give the distance between the two cities. (Hint: The earth's radius is about 3,960 miles.) This is a question similar to what will be on … 
Earth Science
Can you help me find how many hours are received by these degrees of latitude during the winter (see details)? 
trig
if diameter of the circle is 100 cm. and length of the arc forming the angle is 360 cm. Assume that the earth is a perfect sphere of diameter 8000 miles. Find the distance between: Rome, Italy: latitude 42 degrees north Copenhagen, … 
Math
A boat travels 74 miles on a course with direction 34 degrees and then changes its course to travel 58 miles at 53 degrees. How far north and how far east has the boat traveled on its 132mile trip? 
science
Amanda is holding a compass and notices that the north pole of the compass points toward the north pole of the Earth. She is confused because she knows from her science classes that the north poles of two magnets will repel each other. … 
ss
what are latitude and longitude? lines of __________ and lines __________ cross one another. they form a ____________ around the earth. lines of latitude lines of latitude are also called___________ they circle the earth parallel to 
PreCalculus
Two cities are due north of each other. One city has a latitude of 32¢ª45'12" and the second city has a latitude of 51¢ª12'45". Assuming that the earth is a sphere with a radius of 4000 miles, how far apart are the two cities?