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We are given the following information for the triangle:

- Angle \( C = 130.1^\circ \)
- Side \( a = 47.9 \, \text{ft} \)
- Side \( b = 38.3 \, \text{ft} \)

To find the area of a triangle when two sides and the included angle are known, we can use the formula:

\[
\text{Area} = \frac{1}{2} \cdot a \cdot b \cdot \sin(C)
\]

Now, let's calculate the area:

1. Convert the angle \( C = 130.1^\circ \) to radians (since most calculators use radians for trigonometric functions):
   \[
   C_{\text{radians}} = 130.1^\circ \times \frac{\pi}{180^\circ} = 2.2702 \, \text{radians}
   \]

2. Calculate the sine of the angle:
   \[
   \sin(130.1^\circ) = \sin(2.2702) \approx 0.766
   \]

3. Use the formula to calculate the area:
   \[
   \text{Area} = \frac{1}{2} \times 47.9 \times 38.3 \times 0.766
   \]

   \[
   \text{Area} \approx \frac{1}{2} \times 47.9 \times 38.3 \times 0.766 = 704.86 \, \text{square feet}
   \]

So, the area of the triangle is approximately \( 704.86 \, \text{square feet} \).

Would you like further details or have any questions? 

Here are five related questions:
1. How do you find the area if all three sides are known?
2. What happens if one of the angles is a right angle?
3. How would the formula change if the triangle was equilateral?
4. Can this method work for non-Euclidean triangles?
5. What is the importance of converting angles to radians?

**Tip:** Always ensure your calculator is in the correct mode (degrees vs. radians) when working with trigonometric functions involving angles.

Find the area of the triangle ABC. C = 130.1°, a = 47.9 ft, and b = 38.3 ft.

Solve for the area of triangle ABC where C = 130.1°, a = 47.9 ft, and b = 38.3 ft. This solution uses trigonometry and the formula Area = 0.5 * a * b * sin(C). Suitable for high school students in Grades 9-12.

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