How this calculator works
A straight segment is the shortest route between two points. Going by the third vertex must therefore be longer than the opposite side in a non-flat triangle. Checking the two shortest sides against the longest is sufficient. With two sides fixed, rearranging all three inequalities gives an open interval for the third.
Formula
Triangle test: shortest + middle > longest. Third-side bounds: |a-b| < c < a+b.
Worked example
With a = 3 m and b = 4 m, the third side must lie strictly between 1 m and 7 m. A value of 5 m works; 7 m produces a flat shape.
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Frequently asked questions
Why is the lower endpoint excluded?
At c = |a-b| the smaller sides line up inside the largest side, leaving no enclosed area.
Can zero be a side?
No. Triangle sides have positive lengths, even when the lower bound is zero because a equals b.
Does passing the test mean the triangle is right?
No. It only confirms existence. Classify the angles separately or compare the squares of the side lengths.