polygon method

Problem 316
Determine the values of α and θ so that the forces shown in Fig. P-316 will be in equilibrium.
 

Problem 315
The 300-lb force and the 400-lb force shown in Fig. P-315 are to be held in equilibrium by a third force F acting at an unknown angle θ with the horizontal. Determine the values of F and θ.
 

Problem 014
From Fig. P-014, P is directed at an angle α from x-axis and the 200 N force is acting at a slope of 5 vertical to 12 horizontal.

1. Find P and α if the resultant is 500 N to the right along the x-axis.
2. Find P and α if the resultant is 500 N upward to the right with a slope of 3 horizontal to 4 vertical.
3. Find P and α if the resultant is zero.