Question

Two forces with magnitudes of 100 and 50 pounds act on an object at angles of 50° and 160°, respectively. Find the direction and magnitude of the resultant force.

Answer 1

F1 = 100 with 50 degree.
F2 = 50 with 160 degree.

Find the x components of the two forces:
F1_x = 100 * cos(50) = 64.28
F2_x = 50 * cos(160) = -46.98

Find the y components of the two forces:
F1_y = 100 * sin(50) = 76.60
F2_y = 50 * sin(160) = 17.10

The magnitude of the resultant force R will be:
R_x = F1_x + F2_x = 64.28 + (-46.98) = 17.3
R_y = F1_y + F2_y = 76.60 + 17.10 = 93.7

Clearly this is in Quadrant I. So the direction of R is NE.