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When you are solving the problem "how far can you see" over the earth's surface, the solution is very complicated. It's a mess basically.
That's why it's appropriate to use a first-order approximation. Especially because the earth is so large, this approximation is extremely accurate, even for objects the height of Mt. Everest. But there is something tricky here, a square root term. You need this term, flat earthers typically forget it. So their calculations become very off
