DUE: Friday, October $18,2024($Submission to BlackBoard$)$

ALL MATLAB FILES SHOULD BE SUBMITTED AS m$-$file.

A weight $W^{\text{'}}$ is supported by two cables anchored a distance $D$ apart $($see sig F$40$re $P40).$ The cable length $L_{AB}$ is given, but the length $L_{AC}$ is to be selected. Each cable can support a maximum tension force equal to $W.$ For the weight to remain stationary, the total horizontal force and total vertical force must each be zero. This principle gives the equations

$-T_{AB}cos+T_{AC}cos=0$

$T_{AB}sin+T_{AC}sin=W$

We can solve these equations for the tension forces $T_{AB}$ and $T_{AC}$ if we know the angles $$ and $.$ From the law of cosines

$=co{s}^{-1}(\frac{D^2+L_{AB}^2-L_{AC}^2}{2D{L}_{AB}})$

From the law of sines

$=si{n}^{-1}(\frac{L_{AB}sin}{L_{AC}})$

For the given values $D=6ft,L_{AB}=3ft,$ and $W=2000lb,$ use a while loop in MATLAB to find $L_{\text{A}\text{C}\text{m}\text{i}\text{n}},$ the shortest length $L_{AC}$ we can use on the same graph versus $L_{AC}$ for $L_{\text{A}\text{C}\text{m}\text{i}\text{n}}{L}_{AC}6\mathrm{.}7.$

write me a code that I can just copy and paste and please first run it and see if it works. Thank you so much. I promise you I'll give you a like.