The shadow cast by a vertical pillar in Alexandria at noon during the summer solstice is found to be 1/8 the height of the pillar. The distance between Alexandria and Syene is 1/8 the Earth's radius. Is there a geometric connection between these two 1-to-8 ratios?
I already solved this problem. However, there is another part of the problem:
If Earth were smaller than it is, would the shadow of the vertical pillar in Alexandria have been longer or shorter at noon during the summer solstice?
Just a ratio I used to solve the first part.
Pole shadow/Pole height = Alexandria and Syene distance / Earth radius
The Attempt at a Solution
I said the shadow would grow shorter. Since the Earth would be smaller, the distance between Alexandria and Syene would also be smaller. And due to it being a ratio, this would also effect the shadow.
However, I am really not certain of my answer and do not know how I could verify it or if I am correct.