Geometrie-Kreis-Kreissektor (Grad)

$A = \frac{r^{2} \cdot \pi \cdot \alpha }{ 360}$
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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: 03
$\begin{array}{l} \text{Gegeben:}\\\text{Kreiszahl} \qquad \pi \qquad [] \\ \text{Kreisbogen} \qquad b \qquad [m] \\ \text{Radius} \qquad r \qquad [m] \\ \\ \text{Gesucht:} \\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ \alpha = \frac{b\cdot 360}{r\cdot \pi \cdot 2}\\ \textbf{Gegeben:} \\ \pi=3\frac{16}{113} \qquad b=5m \qquad r=200m \qquad \\ \\ \textbf{Rechnung:} \\ \alpha = \frac{b\cdot 360}{r\cdot \pi \cdot 2} \\ \pi=3\frac{16}{113}\\ b=5m\\ r=200m\\ \alpha = \frac{5m\cdot 360}{200m\cdot 3\frac{16}{113} \cdot 2}\\\\\alpha=1,43^{\circ} \\\\ \small \begin{array}{|l|} \hline b=\\ \hline 5 m \\ \hline 50 dm \\ \hline 500 cm \\ \hline 5\cdot 10^{3} mm \\ \hline 5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline r=\\ \hline 200 m \\ \hline 2\cdot 10^{3} dm \\ \hline 2\cdot 10^{4} cm \\ \hline 2\cdot 10^{5} mm \\ \hline 2\cdot 10^{8} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline alpha=\\ \hline 1,43 ° \\ \hline 85,9 \text{'} \\ \hline 5,16\cdot 10^{3} \text{''} \\ \hline 1\frac{42}{71} gon \\ \hline \frac{1}{40} rad \\ \hline \end{array} \end{array}$