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

To find the area of the triangle when you have two sides and the included angle, you can use the formula: \[ \text{Area} = \frac{1}{2} \times a \times c \times \sin(B) \] Here, \(a = 6.1 \text{ ft}\), \(c = 3.8 \text{ ft}\), and \(B = 33^{\circ}\). First, calculate \(\sin(33^{\circ})\): \[ \sin(33^{\circ}) \approx 0.5446 \] Now plug in the values: \[ \text{Area} = \frac{1}{2} \times 6.1 \times 3.8 \times 0.5446 \approx \frac{1}{2} \times 6.1 \times 3.8 \times 0.5446 \] Calculating step-by-step: 1. \(6.1 \times 3.8 = 23.18\) 2. \(23.18 \times 0.5446 \approx 12.628\) 3. \(\frac{1}{2} \times 12.628 \approx 6.314\) Rounding to one decimal place, the area of the triangle is approximately \(6.3 \text{ ft}^2\).