M2 Trigonometry

http://www.mei.org.uk/files/papers/2011_June_m2.pdf

For Question 2iv in the paper above ( mark scheme is at the bottom of the link and questions in the first pages), I don't understand what geometrical calculation you can use.
Please help

There are three forces acting on the beam: Its weight, the tension in the wire and the reaction at the hinge.

The lines of action of 3 forces in equilibrium must go through a common point. I.e. the point P. So AP represents the line of action of the rection at the hinge, and you've worked out its angle to the horizontal in part iii. Hence angle GAP is?

sorry its just in the examiners report(and mark scheme) it says you can use trigonometry as an alternative. I don't see how you can

OK. Refering to diagram:

We know the length of AG.

We can work out the length GP, since GYP is 50 degrees and we know YG.

Tan GAP = GP/AG.

OK. Refering to diagram:

We know the length of AG.

We can work out the length GP, since GYP is 50 degrees and we know YG.

Tan GAP = GP/AG.

Also, why can't you do arcsin(weight divided by the resultant force at the hinge) to find angle GAP

Triangle GAP doesn't form the triangle for forces. You may find it helpful to draw the latter.

ok i drew it out and it wasn't a triangle of forces but is there any general rule for when you can use triangle of forces or do u just draw it and see it and see if it plausible or not because i thought you can use triangle of forces for any 3 forces in equilibrium where their line of action passes through one point

Huh! Don't understand that.

lol just when can you use triangle of forces basically?

When you have three coplanar forces in equilibrium. i.e. nett force is zero. then they can be represented by a "triangle of forces".

Then why can't you use triangle of forces for the 3 coplanar forces in equilibrium in the original question

You can, but the triangle of forces is not the triangle GAP.