1.94: Sector geometry and area

Figure 1 shows $\triangle ABC$ with $AB=22$ cm, $AC=14$ cm and $BC=20$ cm.

(a) Find, to 3 decimal places, the size of each of the three angles of $\triangle ABC$. (5)

The bisector of angle $BAC$ meets $BC$ at $P$.

(b) Find, in cm to 3 significant figures, the length of $AP$. (3)

(c) Find, to the nearest $\text{cm}^2$, the area of $\triangle ABC$. (2)