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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$b = cos \alpha \cdot c$
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
$\begin{array}{l} \text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \text{Hypotenuse} \qquad c \qquad [m] \\ \\ \text{Gesucht:} \\\text{Ankathete zu } \alpha \qquad b \qquad [m] \\ \\ b = cos \alpha \cdot c\\ \textbf{Gegeben:} \\ \alpha=60^{\circ} \qquad c=1\frac{1}{5}m \qquad \\ \\ \textbf{Rechnung:} \\ b = cos \alpha \cdot c \\ \alpha=60^{\circ}\\ c=1\frac{1}{5}m\\ b = cos 60^{\circ} \cdot 1\frac{1}{5}m\\\\b=\frac{3}{5}m \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 60 ° \\ \hline 3,6\cdot 10^{3} \text{'} \\ \hline 2,16\cdot 10^{5} \text{''} \\ \hline 66\frac{2}{3} gon \\ \hline 1,05 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline 1\frac{1}{5} m \\ \hline 12 dm \\ \hline 120 cm \\ \hline 1,2\cdot 10^{3} mm \\ \hline 1,2\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline \frac{3}{5} m \\ \hline 6 dm \\ \hline 60 cm \\ \hline 600 mm \\ \hline 6\cdot 10^{5} \mu m \\ \hline \end{array} \end{array}$