Geometrie-Trigonometrie-Rechtwinkliges Dreieck

$sin \alpha = \frac{a}{c}$
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$a = sin \alpha \cdot c$
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$c = \frac{ a}{sin\alpha }$
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$cos \alpha = \frac{b}{c}$
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$b = cos \alpha \cdot c$
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$c = \frac{ b}{cos \alpha }$
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$tan \alpha = \frac{a}{b}$
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$a = tan \alpha \cdot b$
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$b = \frac{ a}{tan\alpha }$
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Beispiel Nr: 01
$\begin{array}{l} \text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \text{Ankathete zu } \alpha \qquad b \qquad [m] \\ \\ \text{Gesucht:} \\\text{Gegenkathete zu } \alpha \qquad a \qquad [m] \\ \\ a = tan \alpha \cdot b\\ \textbf{Gegeben:} \\ \alpha=30^{\circ} \qquad b=4m \qquad \\ \\ \textbf{Rechnung:} \\ a = tan \alpha \cdot b \\ \alpha=30^{\circ}\\ b=4m\\ a = tan 30^{\circ} \cdot 4m\\\\a=2,31m \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 30 ° \\ \hline 1,8\cdot 10^{3} \text{'} \\ \hline 1,08\cdot 10^{5} \text{''} \\ \hline 33\frac{1}{3} gon \\ \hline 0,524 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 4 m \\ \hline 40 dm \\ \hline 400 cm \\ \hline 4\cdot 10^{3} mm \\ \hline 4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 2,31 m \\ \hline 23,1 dm \\ \hline 231 cm \\ \hline 2,31\cdot 10^{3} mm \\ \hline 2,31\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$