• $A = \frac{r^{2} \cdot \pi \cdot \alpha }{ 360}$
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$r = \sqrt{\frac{A\cdot 360}{\alpha \cdot \pi }}$
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$\alpha = \frac{A\cdot 360}{r^{2} \cdot \pi }$
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$b = \frac{2\cdot r\cdot \pi \cdot \alpha }{ 360}$
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$r = \frac{b\cdot 360}{\alpha \cdot \pi \cdot 2}$
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$\alpha = \frac{b\cdot 360}{r\cdot \pi \cdot 2}$
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Beispiel Nr: 01
$\text{Gegeben:}\\\text{Kreiszahl} \qquad \pi \qquad [] \\ \text{Kreisbogen} \qquad b \qquad [m] \\ \text{Radius} \qquad r \qquad [m] \\ \\ \text{Gesucht:} \\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ \alpha = \frac{b\cdot 360}{r\cdot \pi \cdot 2}\\ \textbf{Gegeben:} \\ \pi=3\frac{16}{113} \qquad b=10m \qquad r=180m \qquad \\ \\ \textbf{Rechnung:} \\ \alpha = \frac{b\cdot 360}{r\cdot \pi \cdot 2} \\ \pi=3\frac{16}{113}\\ b=10m\\ r=180m\\ \alpha = \frac{10m\cdot 360}{180m\cdot 3\frac{16}{113} \cdot 2}\\\\\alpha=3\frac{13}{71}^{\circ} \\\\ \small \begin{array}{|l|} \hline b=\\ \hline 10 m \\ \hline 100 dm \\ \hline 10^{3} cm \\ \hline 10^{4} mm \\ \hline 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline r=\\ \hline 180 m \\ \hline 1,8\cdot 10^{3} dm \\ \hline 1,8\cdot 10^{4} cm \\ \hline 1,8\cdot 10^{5} mm \\ \hline 1,8\cdot 10^{8} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline alpha=\\ \hline 3\frac{13}{71} ° \\ \hline 191 \text{'} \\ \hline 1,15\cdot 10^{4} \text{''} \\ \hline 3,54 gon \\ \hline \frac{1}{18} rad \\ \hline \end{array}$