Find the area of the triangle if \( A=12.8^{\circ}, b=10.8 \) meters, and \( c=6.4 \) meters. Area \( =\square \mathrm{m}^{2} \) (Round to the nearest tenth as needed.)

To find the area of the triangle given angle \( A \) and sides \( b \) and \( c \), we can use the formula: \[ \text{Area} = \frac{1}{2}bc \sin A \] Substituting the values \( b = 10.8 \) meters, \( c = 6.4 \) meters, and \( A = 12.8^{\circ} \): \[ \text{Area} = \frac{1}{2} \times 10.8 \times 6.4 \times \sin(12.8^{\circ}) \] Calculating \( \sin(12.8^{\circ}) \): \[ \sin(12.8^{\circ}) \approx 0.2218 \] Now substitute this value into the area formula: \[ \text{Area} = \frac{1}{2} \times 10.8 \times 6.4 \times 0.2218 \] \[ \text{Area} \approx \frac{1}{2} \times 10.8 \times 6.4 \times 0.2218 \approx 7.6 \text{ m}^2 \] Therefore, the area of the triangle is approximately \( \boxed{7.6} \) square meters (rounded to the nearest tenth).