Diagram Review - A-Level Maths

34645 Q11 (OCR MEI Further Pure Core 2020 November) — image 0

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26418 Q2 (OCR Further Mechanics 2019 June) — image 0

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16386 Q4 (Edexcel M3 2014 June) — image 0

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\begin{tikzpicture}[>=latex, scale=1.5]
    % Configuration variables
    \def\angle{30}      % Inclination angle alpha
    \def\cpos{4.5}      % Distance of point C from origin
    \def\apos{7.0}      % Distance of point A from origin
    \def\totalLen{8.5}  % Length of the incline line

% 1. Draw the horizontal dashed baseline
    \draw[dashed] (0,0) -- (6,0);

% 2. Draw the main inclined plane line
    \draw (0,0) -- (\angle:\totalLen);

% 3. Draw the angle arc and label it alpha
    \draw (1.2, 0) arc (0:\angle:1.2);
    \node at (15:1.5) {$\alpha$};

% 4. Elements on the incline (using a rotated scope for simplicity)
    \begin{scope}[rotate=\angle]
        % Coordinate definitions
        \coordinate (C) at (\cpos, 0);
        \coordinate (A) at (\apos, 0);

% Draw the solid dot at C
        \fill ($(C)+(0,.075)$) circle (2pt);
        
        % Draw the perpendicular tick mark at A
        \draw (A) ++(0, 0.12) -- ++(0, -0.24);

% Draw the thin rod slightly above the incline line
        \draw[thin] (\cpos, 0.08) -- (\apos, 0.08);

% Draw the double-headed dimension arrow for 'l' below the incline
        \draw[<->] (\cpos, -0.4) -- (\apos, -0.4) node[midway, fill=white, inner sep=1pt] {$l$};

% Place labels C and A below their respective points
        \node[below=14pt] at (C) {$C$};
        \node[below=10pt, right=6pt] at (A) {$A$};
    \end{scope}

\end{tikzpicture}

13531 Q3 (OCR MEI S2 2006 January) — image 0

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\begin{tikzpicture}
    \begin{axis}[
        width=12cm, height=9cm,
        axis lines=left,
        xmin=8.5, xmax=27,
        ymin=0, ymax=65,
        % Define ticks based on the image
        xtick={10, 15, 20, 25},
        ytick={0, 10, 20, 30, 40, 50, 60},
        % Remove default labels to place them manually like the image
        xlabel={}, ylabel={},
        axis line style={-latex},
        tick label style={font=\small},
        clip=false
    ]
        % Scatter plot of the data points from the table
        \addplot[only marks, mark=x, mark size=3pt, thick] coordinates {
            (13.3, 9) (17.2, 11) (16.9, 14) (18.7, 26) (18.4, 43)
            (19.3, 25) (23.1, 52) (15.0, 15) (20.6, 10) (14.4, 7)
        };

% Replicating specific label placements
        \node[anchor=east, align=right, font=\small] at (axis cs:8.3, 60) {Nitrous oxide \\ level};
        \node[anchor=west, font=\small] at (axis cs:8.5, 61.5) {$y$};
        \node[anchor=south east, font=\small] at (axis cs:26.5, 0.5) {$x$};
        \node[anchor=north, font=\small] at (axis cs:23.5, -6) {Temperature};

% Creating the axis break (zigzag) on the x-axis
        \draw[white, line width=3pt] (axis cs:9.2, 0) -- (axis cs:9.8, 0);
        \draw[thick] (axis cs:9.0, -1.8) -- (axis cs:9.4, 1.8) -- (axis cs:9.7, -1.8) -- (axis cs:10.1, 1.8);
    \end{axis}
\end{tikzpicture}

42248 Q6 (CAIE M2 2015 November) — image 0

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31313 Q4 (OCR MEI M3 2014 June) — image 0

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31069 Q5 (AQA M3 2015 June) — image 0

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\begin{tikzpicture}[
    >=Straight Barb, % Use a simple V-shaped arrowhead to match the image
    velocity/.style={
        postaction={decorate},
        decoration={
            markings,
            mark=at position 0.55 with {\arrow{>}}
        }
    }
]

% Define the centers of the two circles
    \coordinate (A) at (0,0);
    \coordinate (B) at (2,0);

% Draw the dashed line of centres
    \draw[densely dashed] (-2.2, 0) -- (4.2, 0) node[right, text=black] {\textsf{Line of centres}};

% Draw the two touching circles
    \draw (A) circle (1);
    \draw (B) circle (1);

% Add labels A and B below the circles
    \node at (0, -1.4) {$A$};
    \node at (2, -1.4) {$B$};

% --- Particle A ---
    \def\angleA{115} % Angle for velocity vector A
    
    % Draw velocity vector A
    \draw[velocity] (\angleA:2.8) -- (A);
    \node[right, xshift=2pt] at (\angleA:2.2) {$4\mathrm{\,m\,s^{-1}}$};

% Draw angle arc and label for alpha
    \draw (180:0.5) arc (180:\angleA:0.5);
    \node at (147.5:0.75) {$\alpha$};

% --- Particle B ---
    \def\angleB{100} % Steeper angle for velocity vector B
    
    % Draw velocity vector B
    \draw[velocity] ($(B) + (\angleB:2.8)$) -- (B);
    \node[right, xshift=2pt] at ($(B) + (\angleB:2.2)$) {$2.6\mathrm{\,m\,s^{-1}}$};

% Draw angle arc and label for beta
    \draw ($(B) + (180:0.5)$) arc (180:\angleB:0.5);
    \node at ($(B) + (140:0.75)$) {$\beta$};

\end{tikzpicture}

26074 Q1 (OCR Further Mechanics AS 2018 June) — image 0

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\begin{tikzpicture}[>=latex, line join=round, line cap=round]

% Coordinates
    \coordinate (O) at (0, 0);
    \coordinate (V) at (0, -2.5); % End of dashed vertical line
    \coordinate (P) at (-75:4.5); % Position of mass P

% Draw dashed vertical line
    \draw[densely dashed, semithick] (O) -- (V);

% Draw pendulum string
    \draw[thick] (O) -- (P) node[midway, right=4pt] {$3.2\mathrm{\,m}$};

% Draw pivot point label
    \node[left=2pt] at (O) {$O$};

% Draw angle arc
    \draw (0, -1.2) arc (-90:-75:1.2);

% Draw angle label and curved pointer
    \node (angle_label) at (1.8, -0.8) {$15^\circ$};
    % Use a Bezier curve to match the specific "under-hook" shape from the image
    \draw[->, semithick] (1.7, -1.0) .. controls (1.7, -1.6) and (0.6, -1.6) .. (-80:1.2);

% Draw mass P
    \fill (P) circle (0.15);
    \node[right=4pt] at (P) {$P$};

% Draw velocity vector below P
    % Using coordinates relative to P to maintain the correct slope and position
    \coordinate (v_start) at ($(P) + (1.2, -0.9)$);
    \coordinate (v_end)   at ($(P) + (-0.5, -1.2)$);
    
    \draw[->, semithick] (v_start) -- (v_end);
    
    % Draw velocity label centered below the arrow
    \node[below=2pt] at ($(v_start)!0.5!(v_end)$) {$1.2\mathrm{\,m\,s^{-1}}$};

\end{tikzpicture}

26024 Q7 (OCR Further Statistics AS 2018 June) — image 0

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\begin{tikzpicture}[>=Stealth]
% Define scale: x-axis from 1 to 2.1, y-axis from 6 to 10
\def\xscale{8}
\def\yscale{1.5}

% Draw axes
\draw[->] (0,0) -- (8.8,0) node[right] {$c$};
\draw[->] (0,0) -- (0,6.3);

% x-axis: ranges from 1 to 2, with gridlines
% Map: c=1 -> x=0, c=2 -> x=8, so x = (c-1)*8
% y-axis: m=6 -> y=0, m=10 -> y=6, so y = (m-6)*1.5

% x-axis tick marks and labels
\foreach \c in {1, 1.2, 1.4, 1.6, 1.8, 2} {
  \pgfmathsetmacro{\xpos}{(\c - 1)*8}
  \draw (\xpos, -0.1) -- (\xpos, 0.1);
  \node[below] at (\xpos, -0.1) {$\c$};
}

% y-axis tick marks and labels
\foreach \m in {6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10} {
  \pgfmathsetmacro{\ypos}{(\m - 6)*1.5}
  \draw (-0.1, \ypos) -- (0.1, \ypos);
  \pgfmathsetmacro{\mval}{\m}
  \node[left] at (-0.1, \ypos) {$\pgfmathprintnumber[fixed,precision=1]{\mval}$};
}

% y-axis label
\node[left] at (-0.1, 6.3) {$m$};

% Grid lines (light gray)
\foreach \c in {1, 1.2, 1.4, 1.6, 1.8, 2} {
  \pgfmathsetmacro{\xpos}{(\c - 1)*8}
  \draw[gray!30] (\xpos, 0) -- (\xpos, 6);
}
\foreach \m in {6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10} {
  \pgfmathsetmacro{\ypos}{(\m - 6)*1.5}
  \draw[gray!30] (0, \ypos) -- (8, \ypos);
}

% Data points: (c, m)
% (1.94, 6.5) -> (7.52, 0.75)
\fill (7.52, 0.75) circle (3pt);
% (1.78, 7.2) -> (6.24, 1.8)
\fill (6.24, 1.8) circle (3pt);
% (1.62, 7.4) -> (4.96, 2.1)
\fill (4.96, 2.1) circle (3pt);
% (1.51, 7.6) -> (4.08, 2.4)
\fill (4.08, 2.4) circle (3pt);
% (1.52, 8.3) -> (4.16, 3.45)
\fill (4.16, 3.45) circle (3pt);
% (1.4, 9.7) -> (3.2, 5.55)
\fill (3.2, 5.55) circle (3pt);

\end{tikzpicture}

21210 Q2 (CAIE FP2 2015 June) — image 0

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\begin{tikzpicture}[
    >=Latex,
    line join=round, line cap=round,
    % Define a style for adding an arrow in the middle of a path
    arr/.style={postaction={decorate}, decoration={markings, mark=at position #1 with {\arrow{Latex}}}},
    arr/.default=0.55
]

% Define key coordinates
    \coordinate (Corner) at (5, 0);
    \coordinate (HA) at (5, 1.8);       % Hit point on Wall A
    \coordinate (HB) at (3.8, 0);       % Hit point on Wall B
    
    % The particle path coordinates
    \coordinate (Pstart) at (2.1, 4.7); % Start of the drawn trajectory line
    \coordinate (P) at (2.4, 4.4);      % Position of the particle
    \coordinate (Pend) at (1.5, 2.0);   % End of the drawn trajectory line

% Draw the walls (thick gray fill)
    \fill[gray] (-1.5, -0.2) rectangle (5.2, 0);
    \fill[gray] (5, 0) rectangle (5.2, 4.8);
    
    % Draw the inner solid black boundary lines
    \draw[thick] (-1.5, 0) -- (5, 0) -- (5, 4.8);

% Right angle symbol at the corner
    \draw (4.75, 0) -- (4.75, 0.25) -- (5, 0.25);

% Wall labels
    \node[right] at (5.2, 4.8) {$A$};
    \node[left] at (-1.5, 0) {$B$};

% Draw the trajectory with arrows
    % Segment 1
    \draw[arr=0.6] (Pstart) -- (HA) coordinate[pos=0.6] (Mid1);
    % Segment 2
    \draw[arr=0.55] (HA) -- (HB);
    % Segment 3
    \draw[arr=0.5] (HB) -- (Pend);

% Particle P dot and label
    \fill (P) circle (1.5pt);
    \node[above right, inner sep=1pt] at (P) {$P$};

% Velocity label 'u'
    \node[above right, xshift=1pt] at (Mid1) {$u$};

% Angle alpha
    \draw (5, 2.4) arc (90:135:0.6);
    \node at (4.65, 2.45) {$\alpha$};

\end{tikzpicture}

21025 Q4 (CAIE FP2 2010 June) — image 0

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\begin{tikzpicture}[>=Latex, semithick, line cap=round, line join=round]

% Define radii
    \def\rA{3}   % Radius of circle A (scales to 0.5m)
    \def\rB{1.8} % Radius of circle B (scales to 0.3m)
    
    % Define centers
    \coordinate (A) at (0,0);
    \coordinate (B) at (\rA+\rB, 0);
    \coordinate (Contact) at (\rA, 0);

% Draw the two circles
    \draw (A) circle (\rA);
    \draw (B) circle (\rB);

% Draw horizontal distance arrows
    % Arrow for 0.5 m
    \draw[<->] (A) -- (Contact) node[midway, above] {$0.5\mathrm{\,m}$};
    % Arrow for 0.3 m
    \draw[<->] (Contact) -- (B) node[midway, above] {$0.3\mathrm{\,m}$};

% Draw center labels
    \node[left=2pt] at (A) {$A$};
    \node[right=2pt] at (B) {$B$};

% Draw point P and its label
    \coordinate (P) at (60:\rA);
    \fill (P) circle (1.2pt);
    \node[above right=0pt] at (P) {$P$};

% Draw angular velocity arrow and label
    \draw[->] (155:\rA+0.6) arc (155:215:\rA+0.6) 
        node[pos=0.8, left=2pt] {$\frac{1}{2}t\mathrm{\,rad\,s^{-1}}$};

\end{tikzpicture}

15972 Q5 (Edexcel M3 2022 January) — image 0

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\begin{tikzpicture}[>=latex, line join=round, line cap=round]

% Define parameters for easy adjustment
    \def\HeightA{3.6}       % Height of point A
    \def\Px{3.4}            % X-coordinate of point P
    \def\Pradius{0.14}      % Radius of the black dot P
    
    % Define main coordinates
    \coordinate (O) at (0, 0);
    \coordinate (A) at (0, \HeightA);
    \coordinate (P) at (\Px, \Pradius); % Center of P is above the line by its radius

% Draw horizontal line (ground)
    \draw (-4.5, 0) -- (4.2, 0);

% Draw vertical dashed line
    \draw[densely dashed, semithick] (O) -- (A);

% Draw the solid slanted line
    \draw[semithick] (A) -- (P) node[midway, above right=1pt] {$a$};

% Draw the angle arc and label
    % Calculate the angle of the line AP from the vertical
    \pgfmathsetmacro{\myangle}{atan(\Px / (\HeightA - \Pradius))}
    \begin{scope}[shift={(A)}]
        % Draw arc starting from the vertical dashed line (-90 degrees)
        \draw (0, -1.6) arc (-90:{-90 + \myangle}:1.6);
        % Place the angle label roughly bisecting the arc
        \node at ({-90 + \myangle/2 + 2}:2.0) {$\theta^\circ$};
    \end{scope}

% Labels for A and O
    \node[above=2pt] at (A) {$A$};
    \node[below=2pt] at (O) {$O$};

% Draw the particle P (resting exactly on the horizontal line) and its label
    \fill (P) circle (\Pradius);
    \node[right=3pt] at (P) {$P$};

\end{tikzpicture}

15941 Q1 (Edexcel M3 2017 January) — image 0

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12196 Q6 (OCR S1 2006 June) — image 0

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\begin{tikzpicture}[
    >=Stealth,
    x=0.6cm, 
    y=0.55cm
]

% Grid lines (light) - drawn first so they remain behind the axes
    \foreach \x in {10,11,...,26} {
        \draw[gray!20, very thin] (\x, 0) -- (\x, 10.5);
    }
    \foreach \y in {0,1,...,10} {
        \draw[gray!20, very thin] (10, \y) -- (26.5, \y);
    }

% Axes
    \draw[->, thick] (10, 0) -- (27.5, 0) node[right] {$x$};
    \draw[->, thick] (10, 0) -- (10, 11.5) node[above] {$y$};

% X-axis tick marks and labels
    \foreach \x in {10, 15, 20, 25} {
        \draw[thick] (\x, 0) -- (\x, -0.2) node[below=2pt] {$\x$};
    }

% Y-axis tick marks and labels
    \foreach \y in {0, 5, 10} {
        \draw[thick] (10, \y) -- (9.8, \y) node[left=2pt] {$\y$};
    }

% Data points as crosses using standard TikZ plot marks
    \draw plot[only marks, mark=x, mark options={thick}, mark size=4pt] 
        coordinates {
            (12,10) 
            (13,7.5) 
            (14,6.5) 
            (15,5) 
            (16,4) 
            (21,2.5) 
            (24,1)
        };

\end{tikzpicture}

11566 Q6 (Edexcel M2 2022 January) — image 0

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\begin{tikzpicture}[>=Stealth, scale=0.18]
  % Define coordinates
  % A is at top, ADE goes down-left, ABC goes down-right
  % angle AEC = 90°, EC = 7a, ADE = 24a, ABC = 25a
  % ABD is a semicircular arc of radius 7a
  
  % Place E at origin, with AE vertical and EC horizontal (angle AEC = 90°)
  % AE = 24a, EC = 7a
  % Then AC = 25a (which checks out: 24² + 7² = 576 + 49 = 625 = 25²)
  
  \coordinate (E) at (0, 0);
  \coordinate (A) at (0, 24);
  \coordinate (C) at (7, 0);
  
  % ABC is straight from A to C, length 25a
  % B is on AC such that ABD is a semicircular arc of radius 7a
  % The semicircle has diameter AD where D is on AE
  % Center of semicircle is midpoint of AD
  % AB = arc starts at A, goes through B, ends at D
  % Since ABD is a semicircular arc of radius 7a, the diameter AD = 14a
  % D is on AE at distance 14a from A (since AD = 14a, ADE = 24a, so DE = 10a)
  
  \coordinate (D) at (0, 10); % 24 - 14 = 10 from E, i.e., y=10
  
  % Center of semicircle is midpoint of AD
  \coordinate (O) at (0, 17); % midpoint of A(0,24) and D(0,10)
  
  % B is on line AC. Direction from A to C: (7, -24)/25
  % B is at distance from A along AC such that |OB| = 7 (radius)
  % Parameterize: point on AC = A + t*(C - A) = (7t, 24 - 24t)
  % Distance from O(0,17): sqrt(49t² + (7-24t)²) = 7
  % 49t² + 49 - 336t + 576t² = 49
  % 625t² - 336t = 0
  % t(625t - 336) = 0 => t = 336/625
  
  \coordinate (B) at ({7*336/625}, {24 - 24*336/625});
  % B = (2352/625, 24 - 8064/625) = (3.7632, 11.0976)
  
  % Draw ADE (straight line from A to E)
  \draw[thick] (A) -- (E);
  
  % Draw EC (straight line from E to C)
  \draw[thick] (E) -- (C);
  
  % Draw ABC (straight line from A through B to C)
  \draw[thick] (A) -- (C);
  
  % Draw semicircular arc ABD
  % Center O at (0,17), radius 7a
  % A is at angle 90° from O, D is at angle 270° (or -90°)
  % The semicircle goes from A through B (on the right side) to D
  \draw[thick] (A) arc[start angle=90, end angle=-90, radius=7];
  
  % Labels
  \node[above] at (A) {$A$};
  \node[right] at (B) {$B$};
  \node[right] at (C) {$C$};
  \node[left] at (D) {$D$};
  \node[below left] at (E) {$E$};
  
  % Dimension label for ADE: 24a on the left
  \draw[<->] (-3, 0) -- (-3, 24);
  \node[left] at (-3, 12) {$24a$};
  
  % Dimension label for EC: 7a at bottom
  \draw[<->] (0, -3) -- (7, -3);
  \node[below] at (3.5, -3) {$7a$};
  
  % Right angle mark at E
  \draw (0, 1.5) -- (1.5, 1.5) -- (1.5, 0);
\end{tikzpicture}

11532 Q3 (Edexcel M2 2018 January) — image 0

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11512 Q4 (Edexcel M2 2015 January) — image 0

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\begin{tikzpicture}[line cap=round, line join=round]

% Define parameters for the shape
    \def\a{4}           % Length of the side 'a'
    \def\thetaAngle{40} % Angle \theta from the vertical axis

% Define coordinates based on the geometric properties
    % A is the origin
    \coordinate (A) at (0,0);
    
    % D is straight up from A, at distance 'a'
    \coordinate (D) at (0,\a);
    
    % B is rotated from the vertical by -\theta, at distance 'a' from A
    \coordinate (B) at (90-\thetaAngle:\a);
    
    % F is rotated from the vertical by \theta, at distance 'a' from A
    \coordinate (F) at (90+\thetaAngle:\a);
    
    % C is vertically above B by distance 'a'
    \coordinate (C) at ($(B)+(0,\a)$);
    
    % E is vertically above F by distance 'a'
    \coordinate (E) at ($(F)+(0,\a)$);

% Draw the main solid boundary lines
    \draw[thick] (A) -- (B) -- (C) -- (D) -- (E) -- (F) -- cycle;

% Draw the dashed line of symmetry
    \draw[thick, dashed] (A) -- (D);

% Add vertex labels
    \node[below, yshift=-2pt] at (A) {$A$};
    \node[right, xshift=2pt]  at (B) {$B$};
    \node[above right]        at (C) {$C$};
    \node[above, yshift=2pt]  at (D) {$D$};
    \node[above left]         at (E) {$E$};
    \node[left, xshift=-2pt]  at (F) {$F$};

% Add side length labels 'a'
    % The positions are chosen to match the reference image visually
    \path (A) -- (B) node[midway, below right=1pt] {$a$};
    \path (B) -- (C) node[midway, right=2pt]       {$a$};
    \path (D) -- (C) node[midway, above left=1pt]  {$a$};
    \path (D) -- (E) node[midway, above right=1pt] {$a$};
    \path (E) -- (F) node[midway, left=2pt]        {$a$};
    \path (F) -- (A) node[midway, below left=1pt]  {$a$};

% Add angle arcs and labels for \theta
    \def\arcRad{0.6} % Radius for the angle arcs
    
    % Right angle \theta
    \draw (90-\thetaAngle:\arcRad) arc (90-\thetaAngle:90:\arcRad);
    \node at (90-\thetaAngle/2:\arcRad+0.25) {$\theta$};
    
    % Left angle \theta
    \draw (90:\arcRad) arc (90:90+\thetaAngle:\arcRad);
    \node at (90+\thetaAngle/2:\arcRad+0.25) {$\theta$};

\end{tikzpicture}

7588 Q4 (CAIE S2 2019 June) — image 0

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5898 Q2 (CAIE M2 2017 June) — image 0

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\begin{tikzpicture}[>=Stealth, scale=1.8]
    % Define coordinates based on the 60-degree angle and 0.7m length
    % Let 0.7m be represented by 4 units for better visibility
    \pgfmathsetmacro{\len}{4}
    \coordinate (A) at (0, {\len*cos(60)});
    \coordinate (B) at (0, {-\len*cos(60)});
    \coordinate (P) at ({\len*sin(60)}, 0);
    \coordinate (M) at (0, 0);

% Draw dashed lines
    \draw[thick, dashed] (A) -- (B);
    \draw[thick, dashed] (M) -- (P);

% Draw solid lines with mid-way arrowheads
    \draw[thick, decoration={
        markings,
        mark=at position 0.6 with {\arrow{>}}
    }, postaction={decorate}] (P) -- (A);
    
    \draw[thick, decoration={
        markings,
        mark=at position 0.6 with {\arrow{>}}
    }, postaction={decorate}] (P) -- (B);

% Draw point P
    \fill (P) circle (2pt) node[right=5pt, font=\Large] {$P$};

% Node labels A and B
    \node[left=3pt, font=\Large] at (A) {$A$};
    \node[left=3pt, font=\Large] at (B) {$B$};

% Draw angles with labels
    \draw (0, 1.4) arc (-90:-30:0.6);
    \node at (0.35, 1.25) {\Large $60^\circ$};
    
    \draw (0, -1.4) arc (90:30:0.6);
    \node at (0.35, -1.25) {\Large $60^\circ$};

% Distance labels (0.7 m)
    \node[above] at ($(A)!0.2!(P)+(0.1, .1)$) {$0.7{ m}$};
    \node[below] at ($(B)!0.2!(P)+(0.1, -.1)$) {$0.7{ m}$};

% Force labels (6 N and 4 N)
    \node[below] at ($(P)!0.6!(A)+(0,-.1)$) {$6{ N}$};
    \node[above] at ($(P)!0.6!(B)+(0,.1)$) {$4{ N}$};

\end{tikzpicture}

5763 Q2 (CAIE M2 2010 June) — image 0

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\begin{tikzpicture}[scale=1.2, >=latex]
  % Define the angle of inclination
  \def\angle{35}
  
  % Draw the horizontal ground reference line
  \draw[dashed] (0,0) -- (5,0);
  
  % Draw the inclined plane (ramp)
  \draw[very thick] (0,0) -- (\angle:7.5);
  
  % Draw the 35 degree angle arc and label
  \draw (0.8,0) arc (0:\angle:0.8);
  \node at (17.5:1.2) {$35^\circ$};
  
  % Use a rotated scope to easily draw the triangle relative to the ramp
  \begin{scope}[rotate=\angle]
    % Coordinates on the ramp
    \coordinate (F) at (4.5,0);      % Foot of the altitude
    \coordinate (P) at (4.5,5.5);    % Top vertex (representing 30 cm height)
    \coordinate (V1) at (3.2,0);     % Left base vertex
    \coordinate (V2) at (6.3,0);     % Right base vertex
    
    % Draw the main triangle sides
    \draw[thick] (V1) -- (P) -- (V2);
    
    % Draw the dashed altitude line
    \draw[dashed] (P) -- (F);
    
    % Draw the right-angle symbol at the foot of the altitude
    \draw (F) ++(-0.25,0) -- ++(0,0.25) -- ++(0.25,0);
    
    % Label: 30 cm (parallel to the altitude, on its right side)
    % Drawing from P to F ensures 'above' places the label to the right
    \path (P) -- (F) node[pos=.7, rotate=-55, above, font=\small] {30 cm};
    
    % Label: r cm (parallel to the base, between foot F and vertex V2)
    \path (F) -- (V2) node[midway, rotate=35, above, font=\small, yshift=2pt] {$r$ cm};
  \end{scope}
  
\end{tikzpicture}

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