list Find the area of the triangle. \( \quad \begin{array}{l}\mathrm{B}=33^{\circ}, \mathrm{a}=6.1 \mathrm{ft}, \mathrm{c}=3.8 \mathrm{ft} \\ \text { What is the area of the triangle? } \\ \text { (Do not round until the final answer. Then round to one decimal place as needed.) }\end{array} \)

1. Use the area formula for a triangle with two sides and the included angle: \[ \text{Area} = \frac{1}{2}ac\sin(B) \] 2. Substitute the given values: \[ a = 6.1 \text{ ft}, \quad c = 3.8 \text{ ft}, \quad B = 33^\circ \] \[ \text{Area} = \frac{1}{2} (6.1)(3.8)\sin(33^\circ) \] 3. Multiply \(a\) and \(c\): \[ 6.1 \times 3.8 = 23.18 \] 4. Take half of the product: \[ \frac{1}{2} \times 23.18 = 11.59 \] 5. Calculate \(\sin(33^\circ)\) (ensuring that your calculator is in degree mode): \[ \sin(33^\circ) \approx 0.5446 \] 6. Multiply to find the area: \[ \text{Area} \approx 11.59 \times 0.5446 \approx 6.317 \text{ ft}^2 \] 7. Round to one decimal place: \[ \text{Area} \approx 6.3 \text{ ft}^2 \] \[ \boxed{6.3 \text{ ft}^2} \]