Answer
The law of sines gives two possible candidates for the value of angle C and it is not clear which of the two candidates is the correct value. However, the law of cosines gives a unique solution for the value of the angle C.
Work Step by Step
The law of sines gives two possible candidates for the value of angle C. Since the angle is close to $90^{\circ}$, it is not clear which of the two candidates is the correct value.
However, the law of cosines gives a unique solution for the value of the angle C. Therefore, the law of cosines is a better method in this case.