To find the length of side \( c \) using the Law of Sines, we need to use the relationship given by the Law of Sines:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
From the information given:
- \( A = 72^\circ \)
- \( a = 1246 \) mm
We need additional information about the triangle, specifically the angles or sides \( b \) or \( C \) or \( B \), to use the Law of Sines effectively.
However, if we only have angle \( A \) and side \( a \), we can't find side \( c \) without knowing at least one more angle or side.
Please provide \( B \), \( C \), \( b \), or other relevant information to proceed with the calculation.