Because tension is necessarily positive, I'd write the x-equation of equilibrium as
Tad*sin60º*sin30º - Tac*sin60º*sin30º = 0.
There is no AB term, and no W term.
(This assumes that A is on the y-axis.)
So Tad = Tac
For the y-axis
Tab*cos45º - Tad*sin60º*cos30º + Tac*sin60º*cos30º = 0
0.707*Tab - 0.75*Tad - 0.75*Tad = 0
Tab = 2.123*Tad
Vertically
Tab*sin45º + Tad*cos60º*cos30º + Tac*cos60º*cos30º - 40lb = 0
2.123*Tad + Tad*0.433 + Tad*0.433 = 40 lb
Tad = 40lb / 2.99 = 13.4 lb ◄
Tac = 13.4 lb ◄
Tab = 2.123*13.4lb = 28.4 lb ◄
figure: s.yimg.com/tr/i/0f803deaf4944fffa178bdd3c40e958c_A.png
The weight of the cylinder is 40 lb, the ropes are fixed at B, C, and D.
o x direction force equation of equilibrium? TAB + TAC + TAD + WA = 0
o y direction force equation of equilibrium? TAB + TAC + TAD + WA = 0
o z direction force equation of equilibrium? TAB + TAC + TAD + WA = 0
o Tensile force along AB, TAB ? lb
bTensile force along AC, TAC ? lb
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