You have measured the distance from syene to alexandria to be 493 miles, and you approximate alexandria to be due north of syene. this distance is the same fraction of earth's circumference as the fraction of the full circle from part b is. what is the circumference of earth, as measured in miles?

24650 miles

Explanation:

Eratosthenes found the following equation after measuring the angle of the Sun’s rays off the vertical. The result was an angle of 7.2 degrees. He also knew the circumference of the Earth was a circle of 360 degrees, so he defined the following:

360 degrees/ 7.2 degrees = Earth circumference / distance from Alexandria to Syene

So, since we know distance from Alexandria to Syene is 493 miles, we solve for Earth circumference:

Earth circumference = (360 degrees)*(493 miles) / 7.2 degrees

Earth circumference = 24650 miles.

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