To find the area of triangle \( \triangle ABC \) using the formula \( A = \frac{1}{2} ab \sin C \), we can plug in the values for \( a \), \( b \), and \( \angle C \).
Given:
- \( a = 6 \) yards
- \( b = 12 \) yards
- \( \angle C = 48^\circ \)
First, calculate \( \sin 48^\circ \). Using a calculator:
\[ \sin 48^\circ \approx 0.7431 \]
Now, substitute the values into the area formula:
\[ A = \frac{1}{2} \times 6 \times 12 \times \sin 48^\circ \]
\[ A = \frac{1}{2} \times 6 \times 12 \times 0.7431 \]
Calculating the product:
\[ A = 36 \times 0.7431 \approx 26.6696 \]
Rounding to the nearest square yard:
\[ A \approx 27 \text{ square yards} \]
Thus, the area of triangle \( \triangle ABC \) is approximately \( 27 \) square yards.
The correct response is:
27 yards²