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: 06
$ \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=6m \qquad a=5m \\ \\ \textbf{Rechnung:} \\ sin \alpha = \frac{a}{c} \\ c=6m\\ a=5m\\ sin \alpha = \frac{5m}{6m}\\ \\ \alpha=56,4^{\circ} \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline 6 m \\ \hline 60 dm \\ \hline 600 cm \\ \hline 6\cdot 10^{3} mm \\ \hline 6\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 5 m \\ \hline 50 dm \\ \hline 500 cm \\ \hline 5\cdot 10^{3} mm \\ \hline 5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline alpha=\\ \hline 56,4 ° \\ \hline 3,39\cdot 10^{3} \text{'} \\ \hline 2,03\cdot 10^{5} \text{''} \\ \hline 62,7 gon \\ \hline 0,985 rad \\ \hline \end{array}$