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Problem $3$: As an engineer, you are tasked with providing quality control for the design and construction of a new antenna tower that is to be built. As you review the design calculations, you see that part of the construction plan is to use a turnbuckle to tighten cable $AD$ until it reaches $1300lb$ of tension. You know that the cables that are being used have a maximum capacity of $1800lb$ in tension so the tension in $AD$ seems reasonable. Regardless, you notice the design engineer did not check the resultant forces on the other structural members due to the $1300$ lb on cable $AD.$ Use the equations of equilibrium to determine the forces developed on the other structural elemente

$3\mathrm{.}1)$ Draw a free$-$body diagram of the top of the tower where all the cables are connected $($point A$).$

$3\mathrm{.}2)$ Determine the force in cable $AB.$

$3\mathrm{.}3)$ Determine the force in cable $AC.$

$3\mathrm{.}4)$ Do any of the cables break?

$3\mathrm{.}5)$ As you continue to review the design calculations you see that the antenna tower has a maximum capacity in compression of $2\mathrm{.}1$ kip $.$ Determine the compressive force in the antenna tower.

$3\mathrm{.}6)$ Will the antenna collapse under the load that you found in $3\mathrm{.}5?$

$3\mathrm{.}7)$ Determine the maximum tension in each cable given that the antenna tower can only withstand $2\mathrm{.}1$ kip in compression. Provide the tension in each cable in pounds $($lb$).$ How do i do $3\mathrm{.}7$