In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at an angle of 141d (Alex and Betty's angle). The tire remains stationary in spite of the three pulls. Alex pulls with force Fa of magnitude 208 N, and Charles pulls with force Fc of magnitude 178 N. Note that the direction of Fc is not given. What is the minimum magnitude of Betty's force Fb ?
Sorry don't have a picture :(
The Attempt at a Solution
OK so for this I get
x = -Fa cos(39)[141-180]+0+Fc cos (Theta)
y = Fa sin(39)-Fb+Fc sin (theta)
Solving for Theta I get 24.75240251.
So when I try to plug this into the equation for y to find Fb I find the magnitude to be 56.37042988 (There is no magnitude in the x direction). But this is incorrect. Any idea where I went wrong?