Find the unknown angles in triangle $A B C$, if the triangle exists. \[ A=37.5^{\circ} \quad a=3.4 \quad c=15.6 \] 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 $C=\square^{\circ}$. The measurements for when $B$ is smaller are $B=\square^{\circ}$ and $C=\square^{\circ}$. B. There is only one possible solution for the triangle. The measurements for the remaining angles are $B=\square^{\circ}$ and $\mathrm{C}=$ C. There are no possible solutions for this 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 first calculate angle B using the formula: \(B = \sin^{-1}\left(\frac{a \cdot \sin(A)}{c}\right)\)

Step 3 ：Then, we can calculate angle C using the formula: \(C = 180 - A - B\)

Step 4 ：We need to check if angle B is acute or obtuse. If it's acute, there will be two possible solutions for the triangle. If it's obtuse, there will be only one possible solution.

Step 5 ：The calculated angle B is less than 90 degrees, which means it's acute. Therefore, there are two possible solutions for the triangle. The second possible value for B is the supplement of the first calculated B, and the corresponding value for C is calculated by subtracting A and the second B from 180.

Step 6 ：The calculated second possible value for B is greater than 90 degrees, which means it's obtuse. However, the corresponding value for C is negative, which is not possible for an angle in a triangle. Therefore, there is only one possible solution for the triangle.

Step 7 ：Final Answer: \(\boxed{B=7.6^\circ}\) and \(\boxed{C=134.9^\circ}\). So, the correct choice is B. There is only one possible solution for the triangle. The measurements for the remaining angles are \(\boxed{B=7.6^\circ}\) and \(\boxed{C=134.9^\circ}\).