Walker, Halliday & Resnick — Force and Motion-I: Problem 6

6 In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the overhead view of Fig. 5-20. The tire remains stationary in spite of the three pulls. Alex pulls with force \(\vec{F}_A\) of magnitude 220 N, and Charles pulls with force \(\vec{F}_C\) of magnitude 170 N. Note that the direction of \(\vec{F}_C\) is not given. What is the magnitude of Betty's force \(\vec{F}_B\)?