Find the unknown angles in triangle $A B C$ for each triangle that exists. \[ A=81.5^{\circ} \quad b=9.6 \mathrm{ft} \quad a=11.8 \mathrm{ft} \] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Round to the nearest tenth as needed.) A. There are two possible solutions for the triangle. The measurements for when $\mathrm{B}$ is larger are $\mathrm{B}=\square^{\circ}$ and $\mathrm{C}=\square^{\circ}$. The measurements for when $\mathrm{B}$ is smaller are $\mathrm{B}=\square^{\circ}$ and $\mathrm{C}=\square^{\circ}$. B. There istonly one possible solution for the triangle. The measurements for the remaining angles are $\mathrm{B}=\square^{\circ}$ and $\mathrm{C}=\square^{\circ}$. C. There are no possible solutions for the triangle.

Step 1 ：We are given one angle and two sides of a triangle. We can use the Law of Sines to find the other angles. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides of the triangle.

Step 2 ：We can use this law to find angle B first. Once we have angle B, we can find angle C by subtracting the sum of angles A and B from 180, since the sum of all angles in a triangle is 180 degrees.

Step 3 ：However, the values of B and C seem to be incorrect. The sum of A, B, and C should be 180 degrees, but in this case, it's more than 180 degrees. This is because the sine function can have two possible values - one in the first quadrant and one in the second quadrant. We only considered the value in the first quadrant. We need to consider the value in the second quadrant as well.

Step 4 ：By considering the value in the second quadrant, we find two possible solutions for the triangle. The measurements for when B is larger are \(B=126.4^{\circ}\) and \(C=52.2^{\circ}\). The measurements for when B is smaller are \(B=53.6^{\circ}\) and \(C=125.0^{\circ}\).

Step 5 ：\(\boxed{\text{Final Answer: There are two possible solutions for the triangle. The measurements for when B is larger are } B=126.4^{\circ} \text{ and } C=52.2^{\circ}. \text{ The measurements for when B is smaller are } B=53.6^{\circ} \text{ and } C=125.0^{\circ}.}\)