Solve the triangle. \[ a=6.6 \mathrm{ft}, \quad \mathrm{A}=46^{\circ}, \quad B=66^{\circ} \] Select the correct choice below and fill in the answer boxes within the choice. (Round to the nearest tenth as needed.) A. There is only one possible solution for the triangle. The measurements for the remaining angle $C$, side $c$, and side $b$ are as follows. \[ C=\square^{\circ} \text {. } \] \[ \mathrm{c} \approx \square \mathrm{ft} \] \[ \mathrm{b} \approx \square \mathrm{ft} \] B. There are two possible solutions for the triangle. The measurements for the solution with the longer side $\mathrm{c}$ are as follows. \[ \mathrm{C}=\square^{\circ} \] \[ \mathrm{c} \approx \square \mathrm{ft} \] \[ \mathrm{b} \approx \square \mathrm{ft} \] The measurements for the solution with the shorter side $c$ are as follows. \[ \mathrm{C}=\square^{\circ} \] \[ c \approx \square \mathrm{ft} \] \[ \mathrm{b} \approx \square \mathrm{ft} \] C. There are no possible solutions for this triangle.
Solution
Step 1 ：Given values are side a = 6.6 ft, angle A = 46 degrees, and angle B = 66 degrees.
Step 2 ：Convert angles A and B from degrees to radians. After conversion, A = 0.8028514559173916 radians and B = 1.1519173063162575 radians.
Step 3 ：Calculate angle C using the formula C = π - A - B. After calculation, C = 1.1887246475263237 radians.
Step 4 ：Calculate sides b and c using the formulas b = a * sin(B) / sin(A) and c = a * sin(C) / sin(A). After calculation, b = 8.4 ft and c = 8.5 ft.
Step 5 ：Convert angle C from radians to degrees. After conversion, C = 68.0 degrees.
Step 6 ：Round angle C, side b, and side c to the nearest tenth. After rounding, C = 68.0 degrees, b = 8.4 ft, and c = 8.5 ft.
Step 7 ：\(\boxed{\text{Final Answer: There is only one possible solution for the triangle. The measurements for the remaining angle C, side c, and side b are as follows.}}\)
Step 8 ：\(C=68.0^{\circ}\)
Step 9 ：\(c \approx 8.5 \, \text{ft}\)
Step 10 ：\(b \approx 8.4 \, \text{ft}\)
