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
    $cos \alpha = \frac{b}{c}$
    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: 01
$ \text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \text{Gegenkathete zu }\alpha \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Hypotenuse} \qquad c \qquad [m] \\ \\ c = \frac{ a}{sin\alpha }\\ \textbf{Gegeben:} \\ \alpha=50^{\circ} \qquad a=7m \\ \\ \textbf{Rechnung:} \\ c = \frac{ a}{sin\alpha } \\ \alpha=50^{\circ}\\ a=7m\\ c = \frac{7m}{sin50^{\circ} }\\\\c=9,14m \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 50 ° \\ \hline 3\cdot 10^{3} \text{'} \\ \hline 1,8\cdot 10^{5} \text{''} \\ \hline 55\frac{5}{9} gon \\ \hline 0,873 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 7 m \\ \hline 70 dm \\ \hline 700 cm \\ \hline 7\cdot 10^{3} mm \\ \hline 7\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline 9,14 m \\ \hline 91,4 dm \\ \hline 914 cm \\ \hline 9,14\cdot 10^{3} mm \\ \hline 9,14\cdot 10^{6} \mu m \\ \hline \end{array}$