To solve for side \( a \) using the Law of Sines, we'll start with the given information:
- \( \angle C = 28^\circ \)
- \( c = 28 , \text{m} \)
The Law of Sines states that:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
We only have information about \( \angle C \) and side \( c \). To find side \( a \), we also need the measure of \( \angle A \) or \( \angle B \). Without additional information about the other angles or side lengths, we cannot directly find side \( a \).
If we assume that we have another angle (say, \( \angle A \)), we could proceed with the calculations as follows:
- Calculate \( \sin C \):
\[ \sin 28^\circ \approx 0.4695 \]
- Set up the ratio using the Law of Sines:
\[ \frac{a}{\sin A} = \frac{28}{\sin 28^\circ} \]
- From this, we get:
\[ a = \frac{28 \cdot \sin A}{\sin 28^\circ} \]
- Substituting the value of \( \sin 28^\circ \):
\[ a = \frac{28 \cdot \sin A}{0.4695} \]
- To find \( a \), we'll need the value of \( \sin A \).
If you provide the value for either \( \angle A \) or \( \angle B \), then we can find \( a \). Otherwise, additional details are needed to give a specific numerical answer for side \( a \).
Please provide any missing information, or let me know how you would like to proceed!
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