What is the weight of w to keep the system in equilibrium?

Question

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Answer 1

Let the three tensions from left to right be T1, T2, T3.

Applying Lami's Theorem:

T1 / sin(75) = T2 / sin(150) = 100 / sin(135)

T2 / sin(135) = T3 / sin(105) = W / sin(120)

T2 = 100 sin(150) / sin(135)

T3 = T2 sin(105) / sin(135)

= 100 sin(150) sin(105) / sin^2(135)

W = T3 sin(120) / sin(105)

= 100 sin(150) sin(120) / sin^2(135)

= 86.60 N.