Vectors Question ? ?

Question

Consider four vectors F1, F2, F3, & F4, where their magnitudes are : 44 N, 23 N, 15 N, and 69 N respectively.

Let (measure angle 1) m<1 = 130, m<2 = -150, m<3 = 37 and m<4 = -54, measured from the positive x axis with the counter-clockwise angular direction as positive.

What is the magnitude of the resultant vector F = F1 + F2 + F3 + F4? answer in units of N.

Answer 1

The components are:

F[x] = 44 cos(130) + 23 cos(- 150) + 15 cos(37) + 69 cos(- 54)

F[y]  = 44 sin(130) + 23 sin(- 150) + 15 sin(37) + 69 sin(- 54)

F = sqrt(F[x]^2 + F[y]^2)

= 25.0 N.