Question

In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the picture (the given angle is 134°). The tire remains stationary in spite of the three pulls. Alex pulls with force FA of magnitude 204 N, and Charles pulls with force FC of magnitude 186 N. Note that the direction of FC is not given. What is the magnitude of Betty's force FB if Charles pulls in (a) the direction drawn in the picture or (b) the other possible direction for equilibrium? 

Answer 1

Fa = 204N

Fc = 186N ( direction not given )

Fb = ?

204^2+ + 2*204* cos 134 = 186^2

-283.4 + 7020 =0

= 256 N or

= 27.4 N