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
$\text{Gegeben:}\\\text{Hypotenuse} \qquad c \qquad [m] \\ \text{Gegenkathete zu }\alpha \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ sin \alpha = \frac{a}{c}\\ \textbf{Gegeben:} \\ c=2\frac{1}{2}m \qquad a=1m \\ \\ \textbf{Rechnung:} \\ sin \alpha = \frac{a}{c} \\ c=2\frac{1}{2}m\\ a=1m\\ sin \alpha = \frac{1m}{2\frac{1}{2}m}\\ \\ \alpha=23,6^{\circ} \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline 2\frac{1}{2} m \\ \hline 25 dm \\ \hline 250 cm \\ \hline 2,5\cdot 10^{3} mm \\ \hline 2,5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 1 m \\ \hline 10 dm \\ \hline 100 cm \\ \hline 10^{3} mm \\ \hline 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline alpha=\\ \hline 23,6 ° \\ \hline 1,41\cdot 10^{3} \text{'} \\ \hline 8,49\cdot 10^{4} \text{''} \\ \hline 26,2 gon \\ \hline 0,412 rad \\ \hline \end{array}$