Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let |a| = 30 lb and |b| = 16 lb. Round your answers to one decimal place.)

Question

lal point upward as a 45 degree angle on the first quadrant
lbl point downward as a 30 degree angle on the fourth quadrant

Answer 1

All angles are measured CCW from +x-axis.
Fr = 30Lb[45o] + 16Lb[330o]
X = 30*Cos45 + 16*Cos330 = 35.1 Lbs.
Y = 30*sin45 + 16*sin330 = 13.2 Lbs.

Fr = 35.1 + 13.2i = 37.5Lbs[21o] = Resultant force and direction.

Answer 2

X = 30*Cos(45) + 16*Cos(-30)
Y= 30*Sin(45) + 16*Sin(-30)
Fnet = Sqrt(X^2 +Y^2)

hope that helps, still working on the angle