Determine (a) the required tension in cable AC, knowing that the resultant of the three forces exerted at Point C of boom BC must be directed along BC, (b) the corresponding magnitude of the resultant.

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Using the x and y axes shown:

[latex]\begin{aligned}R_{x}=\Sigma F_{x} & =T_{A C} \sin 10^{\circ}+(50 \,\mathrm{lb}) \cos 35^{\circ}+(75 \,\mathrm{lb}) \cos 60^{\circ} \& =T_{A C} \sin 10^{\circ}+78.458 \,\mathrm{lb} & (1)\R_{y}=\Sigma F_{y} & =(50 \,\mathrm{lb}) \sin 35^{\circ}+(75 \,\mathrm{lb}) \sin 60^{\circ}-T_{A C} \cos 10^{\circ} \R_{y} & =93.631 \,\mathrm{lb}-T_{A C} \cos 10^{\circ} & (2)\end{aligned}[/latex]

(a) [latex]\operatorname{Set} R_{y}=0[/latex] in Eq. (2):

[latex]\begin{aligned}93.631 \,\mathrm{lb}-T_{A C} \cos 10^{\circ} & =0 \T_{A C} & =95.075 \,\mathrm{lb} \quad T_{A C}=95.1 \,\mathrm{lb}\blacktriangleleft\end{aligned}[/latex]

(b) Substituting for [latex]T_{A C}[/latex] in Eq. (1):

[latex]\begin{aligned}R_{x} & =(95.075 \,\mathrm{lb}) \sin 10^{\circ}+78.458 \,\mathrm{lb} \& =94.968 \,\mathrm{lb} \R & =R_{x} & R=95.0 \,\mathrm{lb}\blacktriangleleft\end{aligned}[/latex]

Question 2.129: Determine (a) the required tension in cable AC, knowing that...

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