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To solve this problem, we need to analyze the information provided and use the **Law of Sines** or **Law of Cosines** to determine if a solution exists, and if so, how many solutions there are.

### Given Information
- Side \( a = 55.82 \) mi
- Side \( b = 41.38 \) mi
- Angle \( C = 47.9^\circ \)

### Steps
1. **Determine if there are possible solutions:**
   Using the Law of Sines, we can set up the following relationship:
   \[
   \frac{\sin A}{a} = \frac{\sin C}{c} = \frac{\sin B}{b}
   \]

2. **Calculate \(\sin B\):**
   Using:
   \[
   \frac{\sin B}{b} = \frac{\sin C}{c}
   \]
   we

Solve the triangle, if possible. Given: a = 55.82 mi, b = 41.38 mi, C = 47.9°.

Learn how to solve a triangle with sides a = 55.82 mi, b = 41.38 mi, and angle C = 47.9° using the Law of Sines. This example demonstrates calculating possible values for angles A and B, as well as side c. Suitable for high school trigonometry students.

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