The system is in equilibrium:

Recall from Newton's First and Second Laws the conditions for static equilibrium:

∑F = 0

∑ Forces parallel to direction of rope = 0 --- Eq1

∑Forces perpendicular to direction of rope = 0 --- Eq2

(ii) From Eq1:

[-(Tr)] + [-(W Cos 60°)]+ Tc Cos θ = 0

(-3000N) + (-5000 Cos 60°) + Tc Cos θ° =0

Tc Cos θ = -(-3000N) -(-5000 Cos 60°)

Tc = (3000N + 5000 Cos 60°) / Cos θ

Tc = 6500 / Cos θ

Cos θ = 6500 / Tc ---Eq3

From Eq2:

[-(W Sin 60°)] + Tc Sin θ = 0

5000N Sin 60° = Tc Sin θ

Tc = -5000N Sin 60° / Sin θ

Tc = 4330 / Sin θ

Sin θ = 4330 / Tc ---Eq4

Dividing Eq4 by Eq 3

Sin θ / Cos θ = (4330 / Tc) / (6500/ Tc

Tan θ = 6500/4330

θ = tan^{-1} (4330/6500)

θ = 33.7°

(iii) From Eq3

Tc = 6500 /
Cos θ

Tc = 7810N

From Eq4

Tc = 4330 /
Sin θ

Tc = 7810N