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In any triangle, the sum of the length of any two sides is always greater than the length of the third side.
Here \(AB = c, BC = a\) and \(CA = b\).
Thus the above inequality can be written in the notations as follows:
\(a + b > c\)
\(b + c > a\) and
\(c + a > b\).
Example:
Consider the triangle \(ABC\) with sides measures \(AB = c = 3 cm, BC = a = 4 cm\) and \(AC = b = 5 cm\).
Let's check the triangle inequality for the triangle \(ABC\),
\(a + b = 4 + 5 = 9 > 3 = c\)
\(b + c = 5 + 3 = 8 > 4 = a\) and
\(c + a = 3 + 4 = 7 > 5 = b\).
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