Geometrie-Trigonometrie-Rechtwinkliges Dreieck

$sin \alpha = \frac{a}{c}$
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$a = sin \alpha \cdot c$
1 2 3 4 5 6
$c = \frac{ a}{sin\alpha }$
1 2 3 4 5
$cos \alpha = \frac{b}{c}$
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$b = cos \alpha \cdot c$
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$c = \frac{ b}{cos \alpha }$
1 2 3 4 5
$tan \alpha = \frac{a}{b}$
1 2 3 4 5 6
$a = tan \alpha \cdot b$
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$b = \frac{ a}{tan\alpha }$
1 2 3 4 5 6
Beispiel Nr: 06
$\begin{array}{l} \text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \text{Ankathete zu } \alpha \qquad b \qquad [m] \\ \\ \text{Gesucht:} \\\text{Gegenkathete zu } \alpha \qquad a \qquad [m] \\ \\ a = tan \alpha \cdot b\\ \textbf{Gegeben:} \\ \alpha=20^{\circ} \qquad b=6\frac{1}{2}m \qquad \\ \\ \textbf{Rechnung:} \\ a = tan \alpha \cdot b \\ \alpha=20^{\circ}\\ b=6\frac{1}{2}m\\ a = tan 20^{\circ} \cdot 6\frac{1}{2}m\\\\a=2,37m \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 20 ° \\ \hline 1,2\cdot 10^{3} \text{'} \\ \hline 7,2\cdot 10^{4} \text{''} \\ \hline 22\frac{2}{9} gon \\ \hline 0,349 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 6\frac{1}{2} m \\ \hline 65 dm \\ \hline 650 cm \\ \hline 6,5\cdot 10^{3} mm \\ \hline 6,5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 2,37 m \\ \hline 23,7 dm \\ \hline 237 cm \\ \hline 2,37\cdot 10^{3} mm \\ \hline 2,37\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$