The Greek mathematician Eratosthenes ca 276195 B C measured

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 7.2 degree 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.

Solution

Angle between the two places = 7.2 deg = 0.126 rad

Arc length = 500 miles

Arc length = radius*theta

radius = 500/0.126 = 3968.25 = 3968.3 miles (radius of earth)

circumference of earth = 2pi*radius = 2pi*3968.25 = 24933.275 = 24933.3 miles