Consecutive side length

Geometry Level 5

\(\triangle_{ABC}\) is given that \[3 \times \angle ABC+2 \times \angle BCA=180^{o}\] And three sides of this triangle are 3 consecutive integers. Find the length of these 3 side.

If the length of them are:

\[\begin{eqnarray}\ AB & = & a\\ BC & = & b\\ CA & = & c \end{eqnarray}\] write it as \[a^{b}+c!\] where \(c!\) denotes the factorial notation

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