To find the length of side \( c \) using the Law of Sines, we start with the formula:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
Given that \( A = 72^\circ \) and side \( a = 1246 \) mm, we need more information to find side \( c \) directly. However, we can express \( c \) in terms of another angle and side if we had either angle \( B \) or \( C \).
Without loss of generality, let's denote the other angles as \( B \) and \( C \).
Since we do not have \( B \) or \( C \), we can find the relationship needed to compute side \( c \), knowing \( \sin A \) and using the Law of Sines.
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Calculate \( \sin A \): \[ \sin A = \sin(72^\circ) \approx 0.9511 \]
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Now, using the Law of Sines: \[ \frac{c}{\sin C} = \frac{1246}{0.9511} \]
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To solve for \( c \), we need \( \sin C \): However, we notice we need either \( B \) or \( C \) or additional parameters to proceed.
Due to the lack of additional angles or sides in the problem statement, we cannot find an exact numerical answer for \( c \) without making assumptions or receiving further information. Please provide the missing angles or additional information about triangle characteristics if available. If we assume some angles, we could calculate \( c \) based on those angles, but we need that explicit information.
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