Tikz inclination angle

Question

I am unable to correctly place the alpha angle as well as the rest of this diagram.

My minimal working example (MWE):

\documentclass[tikz,border=5mm]{standalone}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\begin{tikzpicture}[scale=1]
\fill[white] (-1,-5) rectangle (10,5);
\draw[thin] (0,0) grid (17,5);
\draw[line width=2pt] (0,4)--(15,4);
\draw[decorate,decoration={border,amplitude=0.6cm}] (0,4)--(15,4);
\path 
(3,6.5) node{A} 
(8,4.2) node{B} 
(3,4.2) node{C}
(4,5) node{$\theta$}
(4,4)node{$\vec{F}$};
\begin{scope}[rotate around={-30:(2.69,0)}]
\draw[line width=2pt](-1,5)--(5,6);
\shade[ball color=blue!100!green!150,opacity=5](2,6.02)circle (0.5);
\shade[ball color=blue!100!green!150,opacity=5](8,8.29)circle (0.5);
\end{scope}
\draw[blue] (6.5421,4.449225) arc(91:180:0.4515) node[midway,left]{$\alpha$};
\draw (11.49,4.5)--(15,4.5);
\drawline width=2pt,rotate around={30:(5,-1)}--(17,0.8);
\end{tikzpicture}
\end{document}

---

I use \documentclass[12pt]{article}

Answer 1

Something to help the OP in the framing of a simple angle

All we need is to select three coordinates for enclosing the angle -- in this case the coordinates are B, C, D -- in your code you can modify the selection of coordinates as desired

\documentclass[tikz,border=5pt]{standalone}
\usetikzlibrary{calc} 
\usetikzlibrary{angles,intersections,quotes}
%\usepackage{tkz-euclide}
\begin{document}
    \begin{tikzpicture}
        \draw [blue!70!black, thick]
        (0,0)coordinatelabel=-90:A             -- 
            (1,0)coordinatelabel=-90:B         -- 
                (10,0) coordinatelabel=-90:C;
    \draw[blue!70!black, thick]
    (B)                                                             --
        +(20:9cm)coordinate[label=90:D](D);

    \pic[ draw,
            <->,
            >=stealth,
            red!60!black, 
            "$\alpha$"{fill=red!20},
            inner sep=1pt, 
            circle, 
            angle eccentricity=1.1, 
            angle radius = 20mm] 
                        {angle = C--B--D}; 

        \end{tikzpicture}
        \end{document}

Output

Note that changing the sequence of coordinates will effect the angle --initially sequence was CBD now changed to DBC

\begin{tikzpicture}
    \draw [blue!70!black, thick]
    (0,0)coordinate[label=-90:A](A)             -- 
        (1,0)coordinate[label=-90:B](B)         -- 
            (10,0) coordinate[label=-90:C](C);
\draw[blue!70!black, thick]
(B)                                                             --
    +(20:9cm)coordinate[label=90:D](D);

\pic[ draw,
        <->,
        >=stealth,
        red!60!black, 
        "$\alpha$"{fill=red!20},
        inner sep=1pt, 
        circle, 
        angle eccentricity=1.1, 
        angle radius = 20mm] 
                    {angle = D--B--C}; 

    \end{tikzpicture}

Output

Also experimenting with the code will give more insight into placement of the \alpha angle -- for example modifying the eccentricity and angle radius in the above code

angle eccentricity=-1.1, 
                angle radius = 13mm
                            {angle = D--B--C};

will result in

Hope this will help in framing a clear angle

Answer 2

This reminds me of Tilted things in LaTeX but this diagram is less messy.

But the main takeaway is the same: Don't do trigonometry that TikZ can easily do for you!

Instead of a pic we can place a regular circular node along a path, even an inclined one, and TikZ makes sure it's tangent/parallel. (Since the ball doesn't have its own drawn border we can use the original path's \pgflinewidth to adjust its position ever so slightly so that it actually only touches the line. For this we also set outer sep to zero or auto, this also makes sure that the F vector lines start exactly at the ball.)

Giving important coordinates names we can then use the angle library of the angles library to draw the α and θ angles without having to do any calculations. The pic does those for you.

Code

\documentclass[tikz, border=5mm]{standalone}
\usetikzlibrary{angles, arrows.meta, decorations.pathreplacing, quotes}
\tikzset{
  ball above the line/.style={
    sloped, allow upside down, above=.5\pgflinewidth, outer sep=+0pt,
    minimum size=1cm, shape=circle, ball color=blue!50},
  border/.style={
    decoration={name=border, amplitude=.6cm, #1},
    postaction={draw, thin, decorate}}}
\begin{document}
\begin{tikzpicture}[>=Latex, angle radius=1cm, angle eccentricity=1.25]
\draw[line width=2pt, border=reverse path]
  (3, 4) coordinate (left)
  -- coordinate["$B$"] (B)
     node[ball above the line, near end] (right ball) {}
  (15,4) coordinate (right);
\draw[thick]
  (3, 6.5) coordinate["$A$"] (A)
  -- node[ball above the line, near start] (left ball) {}
  (B);
\path[at end]
  (right ball.east) coordinate (rb)
                    edge[->, "$\vec F$"] coordinate (rb-tr) +(30:2)
                    edge[dotted]         coordinate (rb-r)  +( 0:2);
\pic["$\alpha$", draw] {angle=A--B--left};
\pic["$\theta$", draw] {angle=rb-r--rb--rb-tr};
\end{tikzpicture}
\end{document}

Output