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To find the area of triangle ABC given two sides \( a = 45.7 \, \text{ft} \), \( b = 36.4 \, \text{ft} \), and the included angle \( C = 130.9^\circ \), we can use the formula for the area of a triangle when two sides and the included angle are known:

\[
\text{Area} = \frac{1}{2}ab \sin(C)
\]

### Step-by-step:

1. **Given values**:
   - \( a = 45.7 \, \text{ft} \)
   - \( b = 36.4 \, \text{ft} \)
   - \( C = 130.9^\circ \)

2. **Substitute into the formula**:
   \[
   \text{Area} = \frac{1}{2} \times 45.7 \times 36.4 \times \sin(130.9^\circ)
   \]

3. **Calculate \( \sin(130.9^\circ) \)**:
   \[
   \sin(130.9^\circ) \approx 0.7660
   \]

4. **Compute the area**:
   \[
   \text{Area} \approx \frac{1}{2} \times 45.7 \times 36.4 \times 0.7660
   \]
   \[
   \text{Area} \approx 0.5 \times 45.7 \times 36.4 \times 0.7660 \approx 637.4 \, \text{ft}^2
   \]

Thus, the area of the triangle is approximately **637.4 square feet**.

Would you like more details or further clarification? 

Here are five related questions you could explore:
1. How do you calculate the area of a triangle when all three sides are given?
2. What is the Law of Sines and how does it relate to this problem?
3. How can we use the Law of Cosines to find the remaining side of this triangle?
4. How do you calculate the sine of an angle using a calculator?
5. What other methods can be used to find the area of a triangle?

**Tip**: When calculating with angles, make sure your calculator is in degree mode if the angle is given in degrees!

Find the area of the triangle ABC. C = 130.9°, a = 45.7 ft, and b = 36.4 ft.

Learn how to calculate the area of triangle ABC using trigonometry. Given sides a = 45.7 ft, b = 36.4 ft, and angle C = 130.9°, the area is calculated using the formula 0.5 * a * b * sin(C). This is a common geometry problem suitable for high school students in Grades 10-12.

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