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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$c = \frac{ b}{cos \alpha }$
1 2 3 4 5
$tan \alpha = \frac{a}{b}$
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$a = tan \alpha \cdot b$
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$b = \frac{ a}{tan\alpha }$
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Beispiel Nr: 03
$\begin{array}{l} \text{Gegeben:}\\\text{Hypotenuse} \qquad c \qquad [m] \\ \text{Gegenkathete zu }\alpha \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ sin \alpha = \frac{a}{c}\\ \textbf{Gegeben:} \\ c=4,24m \qquad a=3m \\ \\ \textbf{Rechnung:} \\ sin \alpha = \frac{a}{c} \\ c=4,24m\\ a=3m\\ sin \alpha = \frac{3m}{4,24m}\\ \\ \alpha=45^{\circ} \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline 4,24 m \\ \hline 42,4 dm \\ \hline 424 cm \\ \hline 4,24\cdot 10^{3} mm \\ \hline 4,24\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 3 m \\ \hline 30 dm \\ \hline 300 cm \\ \hline 3\cdot 10^{3} mm \\ \hline 3\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline alpha=\\ \hline 45 ° \\ \hline 2,7\cdot 10^{3} \text{'} \\ \hline 1,62\cdot 10^{5} \text{''} \\ \hline 50 gon \\ \hline 0,785 rad \\ \hline \end{array} \end{array}$