1.99: Areas using trigonometry

Figure 1 shows the triangle $ABC$ with $AB=4\text{ cm}$, $BC=5\text{ cm}$ and $\angle BCA=30^\circ$. The point $D$ lies on $AC$ such that $BD=4\text{ cm}$ and angle $BDC$ is obtuse.

Find

(a) the size of angle $BDC$, giving your answer in degrees correct to 1 decimal place, (3)

(b) the length, in cm, of $AD$, giving your answer correct to 3 significant figures, (3)

(c) the area, in $\text{cm}^2$, of triangle $ABD$, giving your answer correct to 3 significant figures. (2)