In Eratosthenes' method of finding the circumference of a planet, when at noon a vertical stick at the Equator casts no shadow, a vertical stick 2,500 kilometers away casts a shadow and makes an angle of 40o with the rays of the Sum. What is the circumference of this planet?

24,901 miles.

Explanation:

The circumference is the distance of the earth that is measured around the poles. Eratosthenes method of finding the circumference of a planet with the sun's rays cast a shadow on the equator a vertical stick of 2,500 km making an angle of 40° with the planet shows a distance of 40,075.017 km. He also estimates that the meridian has a length of 252, 000 stadia. And described these techniques in his book measure of the earth.