The sun angle is formed by the sun's rays and the stick. Getting the shadow length just right is a fuzzy business because not only is the shadow "fuzzy" but it's constantly changing. Getting it when it is at its longest is the goal. That's when the sun is highest in the sky (reaches its zenith.) So with the data I have so far I want to determine the distance between Aruba and White Plains not as the crow flies, but rather when the sun is highest in the sky in both places i.e. north-south distance. Because the earth turns from west to east the sun will be highest in sky first in Aruba, then in White Plains. To find out the north-south distance we will need to find the measurement of the central angle. (see figure below.)
The central angle equals the difference
between the sun angles at city 1 and city 2.
The central angle is the difference between the sun angles in Palm Beach, Aruba and White Plains, NY (City 2.) Why? See this description.
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Also, Eratosthenes measurements, September 21.9.2012, Medvode, Slovenia on Youtube.