I have another question I'm stuck on and have literally no clue to start. It's to do with trigonometry and bearings and I am horrible at worded questions.
"A jet ski travels 200m in a straight line on a bearing of 200°, then 600m in a straight line on a bearing of 060°. Calculate the distance the jet ski must travel, to the nearest m, and the bearing on which it needs to travel to return directly to its start point."
What I've done so far is constructed the triangle, but from there I'm absolutely clueless as to what I need to do.
Once again, thank you all.
(DB, EA, and FC are all parallel)
If only we had $\angle ABC$, we could use the cosine rule to find $AC$! Well, that's exactly what we're going to do:
$$\angle EAB = 160º \ \text{(reflex angles)}$$ $$\angle DBA = 20º \ \text{(alternate angles)}$$ $$ABC = 40º$$
Now, use the cosine rule: $$AC^2 = 200^2 + 600^2 - 2(200)(600) \cos 40º$$ $$AC = \sqrt{200^2 + 600^2 - 2(200)(600) \cos 40º}$$ $$= 465 \ \text{(3 s.f)}$$
Now for part $2$, the bearing of $CA$ is just $360º - \angle FCA$. However, $\angle DBC$ and $\angle FCB$ are corresponding angles, so $\angle FCB = 120º$.
If you just work out $\angle ACB$ (either sine rule or cosine rule works with $AC$ known), you can get the answer.