How do I find components of a vector at a given angle?

[Dylex]

Im a little confused with this question, i can't quite seem to get the hang of it. I understand that you have to use a triangle and i understand that you need to use trigonometry, but what exactly am i even working out? What is the question asking?

The image below shows the question, i am having difficulty mainly with part B (i):

If the image doesn't display go here: http://i.gyazo.com/579170e117432fd87bf8ac5a91c52be3.png

 

[gneill]

You are looking to find the component of the weight vector that is parallel to the slope.

Vector components are usually taken to be perpendicular to each other (in a Cartesian co-ordiinate scheme). So in this case there will be a component perpendicular to the slope and one parallel to the slope, forming a right angle triangle with the weight vector as the hypotenuse.

 

[haruspex]

$m\vec g$ acts vertically downwards, right? But if you decide on a co-ordinate system which has one co-ordinate down the slope (parallel to it) and the other perpendicular to the slope then you can resolve $m\vec g$ into two components in those two directions. The sum of those two, as vectors, is completely equivalent to $m\vec g$.
Do you understand how to find a component of a vector at a given angle to it?