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: 02
$\begin{array}{l} \text{Gegeben:}\\\text{Ankathete zu } \alpha \qquad b \qquad [m] \\ \text{Gegenkathete zu } \alpha \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ tan \alpha = \frac{a}{b}\\ \textbf{Gegeben:} \\ b=8m \qquad a=5m \qquad \\ \\ \textbf{Rechnung:} \\ tan \alpha = \frac{a}{b} \\ b=8m\\ a=5m\\ tan \alpha = \frac{5m}{8m}\\\\\alpha=32^{\circ} \\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline 8 m \\ \hline 80 dm \\ \hline 800 cm \\ \hline 8\cdot 10^{3} mm \\ \hline 8\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 5 m \\ \hline 50 dm \\ \hline 500 cm \\ \hline 5\cdot 10^{3} mm \\ \hline 5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline alpha=\\ \hline 32 ° \\ \hline 1,92\cdot 10^{3} \text{'} \\ \hline 1,15\cdot 10^{5} \text{''} \\ \hline 35,6 gon \\ \hline 0,559 rad \\ \hline \end{array} \end{array}$