Unknown Two Angles

Problem 015
Forces F, P, and T are concurrent and acting in the direction as shown in Fig. P-015.

1. Find the value of F and α if T = 450 N, P = 250 N, β = 30°, and the resultant is 300 N acting up along the y-axis.
2. Find the value of F and α if T = 450 N, P = 250 N, β = 30° and the resultant is zero.
3. Find the value of α and β if T = 450 N, P = 250 N, F = 350 N, and the resultant is zero.