From the information given, the forces are
F1 = −78i + 44j
F2 = 87i + 80j
We would apply the dot product.
F1F2 = <- 78, 44> * <87i, 80j>
F1F2 = - 78(87) + 44(80) = - 6786 + 3520
F1F2 = - 3266
|F1| = √[(- 78)^2 + 44^2] = √8020
|F2| = √[87^2 + 80^2] = √13969
The angle between them is
θ = Cos^-1[F1F2/(|F1||F2|)
θ = Cos^-1(- 3266/√8020 * √13969
θ = Cos^-1(- 0.30856)
θ = 108 degrees
the angle between the cables is 108 degrees