Question

If the distance between a particular lamp post and the equator is 5000 km, find the angle of the sun with respect to the lamp post required for the length of the shadow cast by the lamp post be equal to the length of the lamp post.​

Answer 1

Eratosthenes divided 360° by 7.2° and got 50, which told him that the distance between Alexandria and Syene (500 miles) was 1/50 of the total distance around the Earth. So he multiplied 500 by 50 to arrive at his estimate of the Earth's circumference: 25,000 miles.