As a surveyor, I have to use spherical trigonometry if I measure a large triangle because a triangle on the surface of a sphere has internal angles of more than 180 degrees.
If it is, we better tell the cruise ships that are on around-the-world voyages to stop and come back before they fall off the edge!
But considering that lots of ships have circumnavigated the world, I think they're safe to go all the way around. And if you need more assurance, we have pilots that have flown around the world and satellites orbiting our little spherical planet.
I was never clear on why people thought the world was flat. I thought about the water at the edge. How was it supposed to stay there??? If Earth were flat, the water would just drain off.