physics is annoying

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 the figure. The tire remains stationary in spite of the three pulls. Alex pulls with force of magnitude 227 N, and Charles pulls with force of magnitude 175 N. Note that the direction of Charles' force is not given. What is the magnitude of Betty's force?

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  1. HELP ME !!!!!

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  2. ΣFx= -F(A) •cos47 +F(C)cosφ=0
    ΣFy= F(A) •sin47 +F(C) sinφ –F(B) =0

    -227•0.68 +175•cosφ=0
    227•0.73 +175•sinφ –F(B) = 0

    154.36 =175•cosφ
    cosφ=154.36/175 = 0.88
    φ= 28.36°
    sin28.36°=0.47.

    166 +175•sinφ –F(B) = 0
    F(B) =166 +175•sinφ=
    =166 +175•0.47 = 249 N

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