The Greek mathematician Eratosthenes (ca. 276-195 B.C.) measured the circumference of the earth from the following observations. He noticed that on a certain day the sun shone directly down a deep well in Syene (modern Aswan). At the same time in Alexandria, 500 miles north (on the same meridian), the rays of the sun shone at an angle of 7.2° to the zenith. Use this information and the figure to find the radius of the earth. (Round your answer to the nearest ten miles.)

Question

The Greek mathematician Eratosthenes (ca. 276-195 B.C.) measured the circumference of the earth from the following observations. He noticed that on a certain day the sun shone directly down a deep well in Syene (modern Aswan). At the same time in Alexandria, 500 miles north (on the same meridian), the rays of the sun shone at an angle of 7.2° to the zenith. Use this information and the figure to find the radius of the earth. (Round your answer to the nearest ten miles.)
 
Use this information and the figure to find the circumference of the earth.

Reiny · Accepted Answer

I don't know what your diagram looks like it, but here is page that is similar to your problem
http://www.sciencebuddies.org/science-fair-projects/project_ideas/Astro_p018.shtml

notice that we have a central angle of 7.2°
we can set up a ratio
x/500 = 360°/7.2°
x = 25 000

So the circumference of the earth is 25000 miles according to his calculations.

(modern calculations show the circumference at the equator to be 24902 miles.)

Emma · Answer

The radius would then be 3,979 miles