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An offshore drilling rig is held in place by three tugboats. The tension in one of

the towlines is found to be 750 kN. The figure below is a representation of the

situation as seen from above. All of the measurements given are correct,

however the figure is not to scale and poorly represents dimensions and angles.

85 m

160 m

8

750 kN

T

125 m

130 m

(a) Use the measurements given to determine the angles 0₁ and 0₂ to two

significant figures.

(b) Express the tension forces, T₁ and T₂ in component form.

(6 marks)

(6 marks)

(c) By resolving the forces along x- and y- directions, find two equations

involving the magnitudes of the tension forces, T₁ and T2, on the towlines.

(4 marks)

(d) Express the equations found in part (c) in matrix form, and hence solve the

equations to determine the magnitudes of the tension forces, T₁ and T₂, to

two significant figures.

(14 marks)

Fig: 1