To use the Law of Sines to find the length of side \( c \), we first need to have more information about the triangle, specifically the measures of the other angles or sides. Since we only have one angle (\( \angle A = 54^\circ \)) and one side (\( a = 430 , \text{mm} \)), the Law of Sines states:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
Without additional information, we cannot determine the lengths of sides \( b \) and \( c \) or the angles \( B \) and \( C \). Assuming we could eventually find angle \( C \) or if we have angle \( B \) or some other side, we could rearrange the formula to solve for \( c \):
\[ c = \frac{a \cdot \sin C}{\sin A} \]
If additional information is provided about angles \( B \) or \( C \) or any other sides, we could then solve for \( c \) using the above relationship.
Please provide more details about the triangle, such as any other angles or sides, to proceed with the calculation.