1.84: Areas using trigonometry

In triangle $ABC$, $AB=12\text{ cm}$, $BC=9\text{ cm}$ and angle $BAC=42^\circ$.

(a) Find, in degrees to the nearest $0.1^\circ$, each of the two possible sizes of angle $ABC$. (5)

(b) Find, to 2 significant figures, the smaller of the two possible areas of triangle $ABC$. (3)