Next we are given that the distance between Syene and Alexandria is approximately 575 miles. Let's add this information to our diagram.
If we call the radius of Earth r, then we can write that the distance from the center of the Earth to each of the towns is equal to r.
Notice that we can find the radius of the Earth using the Law of Cosines. We will write the equation according to this law.
575^2= r^2+ r^2-2( r)( r)cos 7.2^(∘)
Let's solve the above equation to find r. Remember that since r needs to be a positive number we will consider only the principal root of r^2.
The radius of Earth is approximately 4579 miles. Finally we can evaluate the circumference of Earth. Let's recall that the circumference of a circle is two times the product of a radius and pi.
C=2π( 4579)≈ 28 771
Using Eratosthenes' Method we found that the circumference of Earth is approximately 28 771 miles.
