Geometrie-Trigonometrie-Rechtwinkliges Dreieck

• $sin \alpha = \frac{a}{c}$
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$a = sin \alpha \cdot c$
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$c = \frac{ a}{sin\alpha }$
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$cos \alpha = \frac{b}{c}$
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$b = cos \alpha \cdot c$
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$c = \frac{ b}{cos \alpha }$
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$tan \alpha = \frac{a}{b}$
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$a = tan \alpha \cdot b$
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$b = \frac{ a}{tan\alpha }$
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Beispiel Nr: 05
$\text{Gegeben:}\\\text{Hypotenuse} \qquad c \qquad [m] \\ \text{Ankathete zu } \alpha \qquad b \qquad [m] \\ \\ \text{Gesucht:} \\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ cos \alpha = \frac{b}{c}\\ \textbf{Gegeben:} \\ c=2\frac{3}{10}m \qquad b=1m \qquad \\ \\ \textbf{Rechnung:} \\ cos \alpha = \frac{b}{c} \\ c=2\frac{3}{10}m\\ b=1m\\ cos \alpha = \frac{1m}{2\frac{3}{10}m}\\\\\alpha=64,2^{\circ} \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline 2\frac{3}{10} m \\ \hline 23 dm \\ \hline 230 cm \\ \hline 2,3\cdot 10^{3} mm \\ \hline 2,3\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 1 m \\ \hline 10 dm \\ \hline 100 cm \\ \hline 10^{3} mm \\ \hline 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline alpha=\\ \hline 64,2 ° \\ \hline 3,85\cdot 10^{3} \text{'} \\ \hline 2,31\cdot 10^{5} \text{''} \\ \hline 71,4 gon \\ \hline 1,12 rad \\ \hline \end{array}$