Geometrie-Trigonometrie-Sinussatz

• $\frac{a}{ sin\alpha} = \frac{b}{ sin\beta }= \frac{c}{ sin\gamma }$
$a = \frac{b\cdot sin\alpha }{ sin\beta }$
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$sin\alpha = \frac{a\cdot sin\beta }{ b}$
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Beispiel Nr: 04
$\text{Gegeben:}\\\text{Winkel} \qquad \beta \qquad [^{\circ}] \\ \text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \text{Länge der Seite} \qquad b \qquad [m] \\ \\ \text{Gesucht:} \\\text{Länge der Seite} \qquad a \qquad [m] \\ \\ a = \frac{b\cdot sin\alpha }{ sin\beta }\\ \textbf{Gegeben:} \\ \beta=150^{\circ} \qquad \alpha=30^{\circ} \qquad b=7\frac{2}{5}m \qquad \\ \\ \textbf{Rechnung:} \\ a = \frac{b\cdot sin\alpha }{ sin\beta } \\ \beta=150^{\circ}\\ \alpha=30^{\circ}\\ b=7\frac{2}{5}m\\ a = \frac{7\frac{2}{5}m\cdot sin30^{\circ} }{ sin150^{\circ} }\\\\a=7\frac{2}{5}m \\\\\\ \small \begin{array}{|l|} \hline beta=\\ \hline 150 ° \\ \hline 9\cdot 10^{3} \text{'} \\ \hline 5,4\cdot 10^{5} \text{''} \\ \hline 166\frac{2}{3} gon \\ \hline 2,62 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline alpha=\\ \hline 30 ° \\ \hline 1,8\cdot 10^{3} \text{'} \\ \hline 1,08\cdot 10^{5} \text{''} \\ \hline 33\frac{1}{3} gon \\ \hline 0,524 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 7\frac{2}{5} m \\ \hline 74 dm \\ \hline 740 cm \\ \hline 7,4\cdot 10^{3} mm \\ \hline 7,4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 7\frac{2}{5} m \\ \hline 74 dm \\ \hline 740 cm \\ \hline 7,4\cdot 10^{3} mm \\ \hline 7,4\cdot 10^{6} \mu m \\ \hline \end{array}$