diff options
Diffstat (limited to 'geometry')
| -rw-r--r-- | geometry/geometry.tex | 1 | ||||
| -rw-r--r-- | geometry/triangle.tex | 41 |
2 files changed, 42 insertions, 0 deletions
diff --git a/geometry/geometry.tex b/geometry/geometry.tex index e52e454..3e50a8e 100644 --- a/geometry/geometry.tex +++ b/geometry/geometry.tex @@ -30,6 +30,7 @@ \subsection{Formeln~~--~\texttt{std::complex}} \sourcecode{geometry/formulars.cpp} \sourcecode{geometry/linesAndSegments.cpp} +\input{geometry/triangle} \sourcecode{geometry/triangle.cpp} \sourcecode{geometry/polygon.cpp} \sourcecode{geometry/circle.cpp} diff --git a/geometry/triangle.tex b/geometry/triangle.tex new file mode 100644 index 0000000..3decd54 --- /dev/null +++ b/geometry/triangle.tex @@ -0,0 +1,41 @@ + +\begin{minipage}[T]{0.27\linewidth} + Generell: + \begin{itemize} + \item $\cos(\gamma)=\frac{a^2+b^2-c^2}{2ab}$ + \item $b=\frac{a}{\sin(\alpha)}\sin(\beta)$ + %\item $b=\frac{a}{\sin(\pi-\beta-\gamma)}\sin(\beta)$ + %\item $\sin(\beta)=\frac{b\sin(\alpha)}{a}$ %asin is not uniquely invertible + \item $\Delta=\frac{bc}{2}\sin(\alpha)$ + \end{itemize} +\end{minipage} +\hfill +\begin{minipage}[B]{0.5\linewidth} + \centering + \begin{tikzpicture}[line cap=round,minimum size=0,x=.7cm,y=0.7cm] + \node[circle,inner sep=0] (AA) at (0,0) {$A$}; + \node[circle,inner sep=0] (BB) at (3,-1) {$B$}; + \node[circle,inner sep=0] (CC) at (3.666667,1) {$C$}; + + \coordinate (A) at (AA.0); + \coordinate (B) at (BB.100); + \coordinate (C) at (CC.210); + + \pic[draw,angle radius=15,pic text=$\gamma$]{angle = A--C--B}; + \pic[draw,angle radius=15,pic text=$\beta$]{angle = C--B--A}; + \pic[draw,angle radius=20,pic text=$\alpha$]{angle = B--A--C}; + + \draw (A) to[edge label={$b$},inner sep=1] (C); + \draw (A) to[edge label'={$c$},inner sep=1.3] (B); + \draw (B) to[edge label'={$a$},inner sep=0.6] (C); + \end{tikzpicture} +\end{minipage} +\hfill +\begin{minipage}[T]{0.16\linewidth} + $\beta=90^\circ$: + \begin{itemize} + \item $\sin(\alpha)=\frac{a}{b}$ + \item $\cos(\alpha)=\frac{c}{b}$ + \item $\tan(\alpha)=\frac{a}{c}$ + \end{itemize} +\end{minipage} |
