If FA 75 lb Fb 80b Fc 43 lb a Write each forces in vector

If F_A - 75 lb, F_b - 80/b, F_c = 43 lb, (a) Write each forces in vector form and find the resultant in the vector form.

Solution

Solution:

All the direction angles are measured from the positive x axis counter clockwise for angle >0 and clockwise for angle <0

For Fa:
Fx = 75 cos 160
Fy = 75 sin 160

For Fb:
Fx = 80 cos (60)
Fy = 80 sin (60)

For Fc:
Fx = 43 cos (-90)
Fy = 43 sin (-90)

So sum of:
Fx = 75 cos (160) + 80 cos (60) + 43 cos (-90) = -30.477
Fy = 75 sin (160) + 80 sin (60) + 43 sin (-90) = 51.933

Magnitude:
F^2 = Fx^2 + Fy^2

F^2 = (-30.477)^2 + (51.933)^2
F = 60.215 N