Question

Estimating the Radius of Earth Eratosthenes, the fifth librarian of Alexandria (230 B.C.), was able to estimate the radius of Earth from the following data: The distance between Egyptian cities of Alexandria and Syrene was 5000 stadia(520 miles). Syrene was located directly south of Alexandria. One summer, at noon, the sun was directly overhead at Syrene, where areas at the same time in Alexandria, the sun at a 7.5˚ angle from the zenith. Eratosthenes reasoned that because the sun is far away, the rays of sunlight that reach Earth must be nearly parallel. From this assumption he concluded tha

Answer 1

that the measure of ∠AOS in the figure must be 7.5˚. Use this information to estimate the radius (to the nearest 10 miles) of Earth.

Answer 2

angle AOS

Answer 3

7.5 DEGREES