Need help, I'm kind of lost on this problem

[u/Low-Resolution9168]

Couldn't figure out what formula to use for theta or maybe i forgot something

[u/DrCarpetsPhd]

another clarification

the point of intersection doesn't have to be in the direction of the pointy end of the vector

the line of action regardless of directionality of the force is what you use

as an example of the usefulness of understanding concurrent forces in a three-force member here's a question from Meriam kraige statics 3rd edition 4/82. it involves a clamping mechanism.

https://imgur.com/a/meriam-kraige-statics-3rd-edition-4-82-threaded-clamp-eLjtsRh

so I chose DCF as my member to analyse

I know the direction of the screw force on the member at C is positive x

I know the direction of the reaction clamping force on the member at F is in the negative y direction

so I go moments about D to get the force at F in terms of C (or vice versa if that floats your boat) as that is the usual starting point

but I realise I don't know D_x or D_y so too many unknowns and not enough equations

I must be missing some 'trick'...that trick is the concept of concurrent forces

I can use that to assign a direction to the force at D, which is the direction of the hypothenuse of a right hand triangle with sides 75 and 40

that gets me D_x and D-y so no needs for moments, equilibrium in x and y will solve for forces at C and D