Geometrie-Trigonometrie-Rechtwinkliges Dreieck

$sin \alpha = \frac{a}{c}$
1 2 3 4 5 6 7
$a = sin \alpha \cdot c$
1 2 3 4 5 6
$c = \frac{ a}{sin\alpha }$
1 2 3 4 5
$cos \alpha = \frac{b}{c}$
1 2 3 4 5 6 7
$b = cos \alpha \cdot c$
1 2 3 4 5 6
$c = \frac{ b}{cos \alpha }$
1 2 3 4 5
$tan \alpha = \frac{a}{b}$
1 2 3 4 5 6
$a = tan \alpha \cdot b$
1 2 3 4 5 6
$b = \frac{ a}{tan\alpha }$
1 2 3 4 5 6
Beispiel Nr: 04
$\begin{array}{l} \text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \text{Gegenkathete zu }\alpha \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Hypotenuse} \qquad c \qquad [m] \\ \\ c = \frac{ a}{sin\alpha }\\ \textbf{Gegeben:} \\ \alpha=30^{\circ} \qquad a=3m \\ \\ \textbf{Rechnung:} \\ c = \frac{ a}{sin\alpha } \\ \alpha=30^{\circ}\\ a=3m\\ c = \frac{3m}{sin30^{\circ} }\\\\c=6m \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 30 ° \\ \hline 1,8\cdot 10^{3} \text{'} \\ \hline 1,08\cdot 10^{5} \text{''} \\ \hline 33\frac{1}{3} gon \\ \hline 0,524 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 3 m \\ \hline 30 dm \\ \hline 300 cm \\ \hline 3\cdot 10^{3} mm \\ \hline 3\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline 6 m \\ \hline 60 dm \\ \hline 600 cm \\ \hline 6\cdot 10^{3} mm \\ \hline 6\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$