Part A $-$ Finding the tension in cable $AC$

Learning Goal:

To apply the condition of equilibrium to three$-$dimensional systems and solve for unknown forces.

As shown, a mass is being lifted by a strut that is supported by two cables $AC$ and $CD.$ The dimensions given are $a=8\mathrm{.}50ft,b=4\mathrm{.}10ft,c=9\mathrm{.}30ft,d=3\mathrm{.}70ft,$ and $e=4\mathrm{.}90ft.($Figure $1)$

Figure

$1$ of $1$

A weight of $180lb$ acts at $C$ on the strut. Find the magnitude of the tension in cable $AC.$

Express your answer to three significant figures and include the appropriate units.

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$T_{AC}=$

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Part B $-$ Finding the unknown weight

What is the weight of an unknown hanging mass when the compressive force in strut $BC$ is $6151$

Express your answer to three significant figures and include the appropriate units.

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Part $C-$ Finding the maximum weight