Part A $-$ Finding the tension in cable $\backslash ($ A C $\backslash )$

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 $\backslash ($ A C $\backslash )$ and $\backslash ($ C D $\backslash ).$ The dimensions given are $\backslash ($ a$=8\mathrm{.}30\backslash$mathrm$\{$ft$\}\backslash ),\backslash ($ b$=5\mathrm{.}10\backslash$mathrm$\{$ft$\},$ c$=9\mathrm{.}90\backslash$mathrm$\{$ft$\},$ d$=3\mathrm{.}70\backslash$mathrm$\{$ft$\}\backslash ),$ and $\backslash ($ e$=4\mathrm{.}50\backslash$mathrm$\{$ft$\}\backslash ).($Figure $1)$

Figure

A weight of $125$ lb acts at $\backslash ($ C $\backslash )$ on the strut. Find the magnitude of the tension in cable $\backslash ($ A C $\backslash ).$ Express your answer to three significant figures and include the appropriate units.

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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 $\backslash ($ B C $\backslash )$ is $645$ lb $?$

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

View Available Hint$($s$)$ Part C $-$ Finding the maximum weight

Find the maximum weight that the cable and strut system can support if the magnitude of the compressive force in the strut cannot exceed $1100$ lb and the magnitude of tension in the cables cannot exceed $300$ lb $.$

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

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