Lateen sails work in much the same way that most other triangular sails work.
If the wind is behind the sail it will push the boat/ship/craft/vessel forward.
But suppose that the boat is at right angles to the wind. What happens then?
The sail is let out on the side of the boat that away from the wind. The wind blows against the surface of the sail. It might strike the surface at an angle of, say 140o. The wind escapes from the side of the sail at its widest point, and the boat slides towards the opposite direction i.e. the direction the boat is facing, its keel preventing it from simply moving/sliding in the water in a path directly away from the wind
This is a basic explanation of how a Lateen sail works.
Of course, it doesn't fully explain how a boat with Lateen sails can sail almost directly into the wind!
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