Left Hand Wall

[math]x=-y\ cot\ 29.5^{\circ}+0.09156[/math]

Parameterizing this

[math]r\mapsto \{-y\ cot\ 29.5^{\circ}+0.09156,y,0 \}[/math]

[math]t\mapsto \{t\ cos\ 29.5^{\circ}+0.09156,-t\ sin\ 29.5^{\circ},0 \}[/math]

where the negative sign is applied to the sine function by the even odd relationships of cosine and sine, i.e. ( sin(-t)=-sin(t), cos(-t)=cos(t)) and the fact that the y component is in the 4th quadrant.

[math] \begin{bmatrix} x'' \\ y'' \\ z'' \end{bmatrix}= \begin{bmatrix} cos\ 6^{\circ} & -sin\ 6^{\circ} & 0 \\ sin\ 6^{\circ} & cos\ 6^{\circ} & 0 \\ 0 & 0 & 1 \end{bmatrix} \cdot \begin{bmatrix} x' \\ y' \\ z' \end{bmatrix}[/math]

[math] \begin{bmatrix} x'' \\ y'' \\ z'' \end{bmatrix}= \begin{bmatrix} cos\ 6^{\circ} & -sin\ 6^{\circ} & 0 \\ sin\ 6^{\circ} & cos\ 6^{\circ} & 0 \\ 0 & 0 & 1 \end{bmatrix} \cdot \begin{bmatrix} t\ cos\ 29.5^{\circ}+0.09156 \\ -t\ sin\ 29.5^{\circ} \\ 0 \end{bmatrix}[/math]

[math] \begin{bmatrix} x'' \\ y'' \\ z'' \end{bmatrix}= \begin{bmatrix} 0.09156\ cos\ 6^{\circ}+t\ cos\ 6^{\circ}cos\ 29.5^{\circ}+t\ sin\ 6^{\circ}sin\ 29.5^{\circ} \\ -t\ cos\ 6^{\circ}sin\ 29.5^{\circ}+0.09156\ sin\ 6^{\circ}+t\ cos\ 29.5^{\circ}sin\ 6^{\circ} \\ 0 \end{bmatrix}[/math]

[math] \begin{bmatrix} x'' \\ y'' \\ z'' \end{bmatrix}= \begin{bmatrix} 0.09156\ cos\ 6^{\circ}+t\ (cos\ 6^{\circ}cos\ 29.5^{\circ}+ sin\ 6^{\circ}sin\ 29.5^{\circ}) \\ 0.09156\ sin\ 6^{\circ}-t\ (cos\ 6^{\circ}sin\ 29.5^{\circ}-sin\ 6^{\circ} cos\ 29.5^{\circ}) \\ 0 \end{bmatrix}[/math]

[math] \begin{bmatrix} x'' \\ y'' \\ z'' \end{bmatrix}= \begin{bmatrix} 0.09156\ cos\ 6^{\circ}+t\ cos\ (6^{\circ} -29.5^{\circ}) \\ 0.09156\ sin\ 6^{\circ}+t\ sin\ (6^{\circ}-29.5^{\circ}) \\ 0 \end{bmatrix}[/math]

[math] \begin{bmatrix} x'' \\ y'' \\ z'' \end{bmatrix}= \begin{bmatrix} 0.09156\ cos\ 6^{\circ}+t\ cos\ (-23.5^{\circ}) \\ 0.09156\ sin\ 6^{\circ}+t\ sin\ (-23.5^{\circ}) \\ 0 \end{bmatrix}[/math]

[math] \begin{bmatrix} x'' \\ y'' \\ z'' \end{bmatrix}= \begin{bmatrix} 0.09156\ cos\ 6^{\circ}+t\ cos\ 23.5^{\circ} \\ 0.09156\ sin\ 6^{\circ}-t\ sin\ 23.5^{\circ} \\ 0 \end{bmatrix}[/math]

Using the equation for y we can solve for t

[math]y''=0.09156\ sin\ 6^{\circ}-t\ sin\ 23.5^{\circ} \Rightarrow t=\frac{-(y''-0.09156 sin 6^{\circ})}{sin 23.5^{\circ}}[/math]

Substituting this into the expression for x

[math]x''=0.09156\ cos\ 6^{\circ}+t\ cos\ 23.5^{\circ}[/math]

[math]x''=0.09156\ cos\ 6 ^{\circ}+\frac{-(y''-0.09156 sin 6 ^{\circ})}{sin 23.5^{\circ}}(cos 23.5^{\circ})[/math]

[math]x''=0.091058+\frac{y''-.0095706 }{-0.398749} (.917060)[/math]

[math]x''=0.091058+(y''-.0095706 ) (-2.299843)[/math]

[math]x''=-2.299843\ y''+.022011+.091058[/math]

[math]x''=-2.299843\ y''+.113069[/math]

leftRotated = 
  ContourPlot[x2 == -2.299843 y + .113069, {y, -1, 1}, {x2, 0, 1.8}, 
   Frame -> {True, True, False, False}, 
       PlotLabel -> 
    "Right side limit of DC as a function of X and Y", 
   FrameLabel -> {"y (meters)", "x (meters)"}, 
   ContourStyle -> Black, 
       PlotLegends -> Automatic];