Have you ever noticed a jet stream that looked like it was going straight up? Have you wondered if it might be a rocket? Due to the curvature of the earth, a plane coming in your direction just appears to be going striaght up. If the earth was flat, the jet would look more like a point getting closer rather than a jet stream line going straight up. Just imagine you were a tiny point standing on a tennis ball and looking at another point circling the ball and coming in your direction. It would like like it is going straight up, not straight at you. Our world is smaller than we may think! Using the same sort of logic with respect to shadows, the ancient Greeks figured out not only that the world was round, but also with simple trigonometry they calculated the diameter of the earth.
By the way, today (March 20, 2018) is the equinox. The sun rises due east, goes directly over head, and sets due west.