To find the area of triangle ABC using the formula \( A = \frac{1}{2}ab \sin C \), we can plug in the values:
- \( a = 6 \) yards
- \( b = 12 \) yards
- \( C = 48^\circ \)
First, we need to calculate \( \sin 48^\circ \). Using a calculator:
\[ \sin 48^\circ \approx 0.7431 \]
Now substitute the values into the area formula:
\[ A = \frac{1}{2} \cdot 6 \cdot 12 \cdot \sin 48^\circ \] \[ A = \frac{1}{2} \cdot 6 \cdot 12 \cdot 0.7431 \] \[ A = 3 \cdot 12 \cdot 0.7431 \] \[ A = 36 \cdot 0.7431 \approx 26.676 \]
Rounding to the nearest square yard, we get:
\[ A \approx 27 \text{ yards}^2 \]
Thus, the area of triangle ABC is approximately 27 yards².