Question 760034
The drawing below is not to scale, because a {{{7.2^o}}} angle would be hard to see. I had to draw a larger angle, which makes the distance between Syene and Alexandria look larger.
{{{drawing(450,300,-220,110,-110,110,
circle(0,0,100),
line(0,0,-100,0),line(0,0,-94,34.2),
red(line(-220,0,-100,0)),red(line(-220,34.2,-94,34.2)),
locate(-97,-1,S),locate(-90,45,A),
green(line(-94,34.2,60,34.2)),blue(line(-94,34.2,-182,68.4)),
locate(-40,12,theta),locate(-134,46,theta),locate(-65,34,theta),
locate(3,5,C)
)}}} 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 {{{theta=7.2^o}}}
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 {{{theta}}} have the same measure, including angle ACS, so the distance between Syena and Alexandria (the short arc AS) represents
{{{7.2^o/360^2=1/20}}} of the circumference of Earth.
{{{circumference/50=500miles}}} --> {{{circumference=50*500miles}}} --> circumference of Earth = {{{highlight(25000miles)}}}