M1 Forces past paper question

https://www.mathsgenie.co.uk/alevel/m1jan2010ans.pdf

For q3, if I use the sine rule I get 20sqrt3/3 instead of 20sqrt3. Any reason why this is the case? I prefer using the method stated in the solution but I'm wondering if i'm using the sine rule incorrectly?

Post your working please

Sure. 20/sin60 = BC / sin 30

BC = 20sin30/sin60

I think your triangle of forces is not correct - I did not get that

Hmm that'd probably be it. Have you got a diagram of what it shoud be like?

Only on a scrap of paper - do your arrows go round the triangle?

Ehm I think so. I've got an arrow going from C to B, another going from C to A and one going from A to B. Oh wait that's horribly wrong. I'll try to fix it.

I've got gravity going down then the bottom of that joins to the Tension we want [angle between is 30] then at the top of the tension is the 20N force.

I'm still really confused. When I draw that, I don't get the tension force going from head to tail.

Arrow on gravity is going downwards then Tension arrow is up and right from the bottom of the gravity arrow and the 20N is up and left to join the tail of the gravity.

I think I might have misunderstood the concept then. I've drawn that but it doesn't make sense to me. Shouldn't the resultant forces go from the tail of the tension to its head. In this case we're going from its head to tail.

It's a triangle of forces - they are in equilibrium .. the arrows should go round the triangle. I think you are confusing with something else..

Yeah haha you're right. https://www.examsolutions.net/tutorials/equilibrium-particle/?level=A-Level&board=Edexcel&module=Mechanics%20A-Level&topic=1637

If you skip to about 2mins 50 I make that mistake he talks about . Thanks for helping me realise.

That's why it's easier to resolve horizontally here as this only involves two forces