1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
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}
|