SOLUTION: At a certain day, the sun shone directly on a deep well in Syene. At the same time in Alexandria, 500 miles north , the rays of the sun shone at an angle of 7.2degrees to the zenit

Question 760034: At a certain day, the sun shone directly on a deep well in Syene. At the same time in Alexandria, 500 miles north , the rays of the sun shone at an angle of 7.2degrees to the zenith. find the radius and circumference of the earth.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The drawing below is not to scale, because a angle would be hard to see. I had to draw a larger angle, which makes the distance between Syene and Alexandria look larger.
C is the center of Earth; A is Alexandria; S is Syene; the red lines represent sun rays, and the blue line going away from A is the direction to the zenith from Alexandria.
So the angle between the red and blue lines is
We can draw sun rays as parallel lines because the sun is very far away and much larger than Earth.
Because those ray are parallel, all those angles labeled as have the same measure, including angle ACS, so the distance between Syena and Alexandria (the short arc AS) represents
of the circumference of Earth.
--> --> circumference of Earth =
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