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[–]CompleteDoubterII[S] 2 insightful - 2 fun2 insightful - 1 fun3 insightful - 2 fun -  (4 children)

If the length of one side of a right triangle is fixed

Yes, your argument makes sense and is intuitive from there. But it requires one side's length to be fixed, so it's doesn't prove that only the angles generate a fixed ratio, and no intuition from that argument comes to me that can prove only the angles generate the ratio.

[–][deleted]  (3 children)

[deleted]

    [–]CompleteDoubterII[S] 1 insightful - 1 fun1 insightful - 0 fun2 insightful - 1 fun -  (2 children)

    Not to me.

    [–][deleted]  (1 child)

    [deleted]

      [–]CompleteDoubterII[S] 1 insightful - 1 fun1 insightful - 0 fun2 insightful - 1 fun -  (0 children)

      Yes, on a flat surface. But that's to do with the real world, and not with right-angled triangles.