Geometrie-Trigonometrie-Rechtwinkliges Dreieck


  • $sin \alpha = \frac{a}{c}$
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    $a = sin \alpha \cdot c$
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    $c = \frac{ a}{sin\alpha }$
    1 2 3 4 5
    $cos \alpha = \frac{b}{c}$
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    $b = cos \alpha \cdot c$
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    $c = \frac{ b}{cos \alpha }$
    1 2 3 4 5
    $tan \alpha = \frac{a}{b}$
    1 2 3 4 5 6
    $a = tan \alpha \cdot b$
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    $b = \frac{ a}{tan\alpha }$
    1 2 3 4 5 6

Beispiel Nr: 02
$ \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=3m \qquad b=2m \qquad \\ \\ \textbf{Rechnung:} \\ cos \alpha = \frac{b}{c} \\ c=3m\\ b=2m\\ cos \alpha = \frac{2m}{3m}\\\\\alpha=48,2^{\circ} \\\\\\ \small \begin{array}{|l|} \hline c=\\ \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 b=\\ \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 48,2 ° \\ \hline 2,89\cdot 10^{3} \text{'} \\ \hline 1,73\cdot 10^{5} \text{''} \\ \hline 53,5 gon \\ \hline 0,841 rad \\ \hline \end{array}$