Geometrie-Dreieck-Allgemeines Dreieck

$A = \frac{g \cdot h}{2}$
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$g = \frac{A\cdot 2}{ h}$
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$h = \frac{A\cdot 2}{ g}$
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$A =\frac{1}{2}\cdot a\cdot b\cdot sin(\gamma)$
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$U = a+b+c$
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Beispiel Nr: 06
$\begin{array}{l} \text{Gegeben:}\\\text{Winkel gamma} \qquad \gamma \qquad [^{\circ}] \\ \text{Länge der Seite} \qquad b \qquad [m] \\ \text{Länge der Seite} \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Fläche} \qquad A \qquad [m^{2}] \\ \\ A =\frac{1}{2}\cdot a\cdot b\cdot sin(\gamma)\\ \textbf{Gegeben:} \\ \gamma=120^{\circ} \qquad b=0,002m \qquad a=\frac{2}{5}m \qquad \\ \\ \textbf{Rechnung:} \\ A =\frac{1}{2}\cdot a\cdot b\cdot sin(\gamma) \\ \gamma=120^{\circ}\\ b=0,002m\\ a=\frac{2}{5}m\\ A =\frac{1}{2}\cdot \frac{2}{5}m\cdot 0,002m\cdot sin(120^{\circ} )\\\\ A=0,000346m^{2} \\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline 0,002 m \\ \hline \frac{1}{50} dm \\ \hline \frac{1}{5} cm \\ \hline 2 mm \\ \hline 2\cdot 10^{3} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline \frac{2}{5} m \\ \hline 4 dm \\ \hline 40 cm \\ \hline 400 mm \\ \hline 4\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline gamma=\\ \hline 120 ° \\ \hline 7,2\cdot 10^{3} \text{'} \\ \hline 4,32\cdot 10^{5} \text{''} \\ \hline 133\frac{1}{3} gon \\ \hline 2,09 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline 0,000346 m^2 \\ \hline 0,0346 dm^2 \\ \hline 3,46 cm^2 \\ \hline 346 mm^2 \\ \hline 3,46\cdot 10^{-6} a \\ \hline 3,46\cdot 10^{-8} ha \\ \hline \end{array} \end{array}$