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: 05
$\begin{array}{l} \text{Gegeben:}\\\text{Ankathete zu } \alpha \qquad b \qquad [m] \\ \text{Gegenkathete zu } \alpha \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ tan \alpha = \frac{a}{b}\\ \textbf{Gegeben:} \\ b=4m \qquad a=2m \qquad \\ \\ \textbf{Rechnung:} \\ tan \alpha = \frac{a}{b} \\ b=4m\\ a=2m\\ tan \alpha = \frac{2m}{4m}\\\\\alpha=26,6^{\circ} \\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline 4 m \\ \hline 40 dm \\ \hline 400 cm \\ \hline 4\cdot 10^{3} mm \\ \hline 4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 2 m \\ \hline 20 dm \\ \hline 200 cm \\ \hline 2\cdot 10^{3} mm \\ \hline 2\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline alpha=\\ \hline 26,6 ° \\ \hline 1,59\cdot 10^{3} \text{'} \\ \hline 9,56\cdot 10^{4} \text{''} \\ \hline 29,5 gon \\ \hline 0,464 rad \\ \hline \end{array} \end{array}$