First, let us find the angles between tensions T and the ceiling. This can be done by cosine rule. We know the sides - 2, 3, and 4 m. Let us find the angle between T1 and the blue line:
22=42+32−2⋅4⋅3cosθ1, cosθ1=2⋅3⋅442+32+22=0.875, θ1=29°. Let us find the angle between T2 and the blue line:
32=42+22−2⋅4⋅2cosθ2, θ2=46.6°. Now write the equilibrium of forces along vertical and horizontal axes:
y:T2sinθ2+T1sinθ1−mg=0,x:−T2cosθ2+T1cosθ2=0.T1=69.5 N.T2=88.5 N. The equations were solved for T1 and T2 assuming that g=9.8 m/s2
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