#### 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.