M2 Statics help please

I am really struggling with the statics of rigid bodies section in M2. I have attached a question that I have got some what lost in (also attached working, sorry if it's hard to follow).

Any help would be greatly appreciated thanks

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I can't quite figure out what you are doing.

Did you notice you could find the angle the rope makes with the string?

Also, I always just teach to find the vertical and horizontal components at the hinge and then use pythagoras to find the magnitude and a nice right angle triangle to find the angle.

I have attached what I have done, hopefully you can understand. I always get my students to draw out the plank writing all the perpendicular forces on it to make do moments easier.

Thanks a lot I can see where I am going wrong now. I spotted everything but then I doubted myself and made many stupid mistakes.

also look at this link

http://www.madasmaths.com/archive/maths_booklets/mechanics/m2_equilibrium_of_rigid_bodies.pdf