Bearing and Distances Question

Question

I don't really understand this question. Please help me, a diagram would be appropriate too.

A plane flies from $A$ to $B$, a distance of $120~\text{km}$ on a bearing of $035^\circ$. It then changes direction and flies to $C$, a further distance of $200 ~\text{km}$ on a bearing of $125^\circ$.

Find:

(i) the distance $AC$, to the nearest kilometer;

(ii) the bearing of $C$ from $A$;

(iii) If the plane now flies directly from $C$ to $A$, what is the shortest distance between the plane and $B$?

I tried to solve (i) and (ii) but (iii) makes no sense at all.

Answer 1

Hints:

1. What do you notice about the degrees?
2. Use vectors to express each of the components, then close the resulting figure. What do you notice?
3. Once you find the distance between $\overline {AC}$, the bearing will follow.