Unknown Two Forces

Problem 271
The three forces in Fig. P-270 create a vertical resultant acting through point A. If T is known to be 361 lb, compute the values of F and P.
 

Problem 270
The three forces shown in Fig. P-270 are required to cause a horizontal resultant acting through point A. If F = 316 lb, determine the values of P and T. Hint: Apply M_R = ΣM_B to determine R, then M_R = ΣM_C to find P, and finally M_R = ΣM_D or R_y = ΣY to compute T.
 

Problem 242
Find the value of P and F so that the four forces shown in Fig. P-242 produce an upward resultant of 300 lb acting at 4 ft from the left end of the bar.