Question

If the resultant force of the shown force system , acting on the cable-post , is directed vertically downward , determine the magnitudes of the force F and the resultant force. http://postimg.org/image/x7995jb2v/

Answer 1

you will need to sum forces in the x-direction and the y-direction, using sin() and cos(),
like this:
x-direction:
0 = -130*cos(27) + 50*cos(17) + other forces I didn't do

y-direction:
0 = -130*sin(27) - 50*sin(17) + other forces I didn't put in

does this get you started in the right direction?
so finish summing the forces in the x and y direction, i've started it for you, you need to finish the two equations above. once they are finished, you will be able to solve for force F by using algebra in either equation, x or y.