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As many as you like but they will all be scalene triangles from the given interior angles that add up to 180 degrees.
Only 3: [1,4,4], [2,3,4] and [3,3,3] Remeber that the sum of the lengths of any two sides MUST be greater than the third side. So triangles like [1,2,6] cannot exist.
How many triangles exist with the given side lengths 3in, 4in, 2in
Yes, they do exist. And the question is ... ?