document.write( "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.
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Algebra.Com's Answer #462396 by KMST(5328) $\"\"$ $\"About$

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The drawing below is not to scale, because a $\"7.2%5Eo\"$ angle would be hard to see. I had to draw a larger angle, which makes the distance between Syene and Alexandria look larger.
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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.
\n" ); document.write( "So the angle between the red and blue lines is $\"theta=7.2%5Eo\"$
\n" ); document.write( "We can draw sun rays as parallel lines because the sun is very far away and much larger than Earth.
\n" ); document.write( "Because those ray are parallel, all those angles labeled as $\"theta\"$ have the same measure, including angle ACS, so the distance between Syena and Alexandria (the short arc AS) represents
\n" ); document.write( " $\"7.2%5Eo%2F360%5E2=1%2F20\"$ of the circumference of Earth.
\n" ); document.write( " $\"circumference%2F50=500miles\"$ --> $\"circumference=50%2A500miles\"$ --> circumference of Earth = $\"highlight%2825000miles%29\"$ \n" ); document.write( "

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