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{Ankathete zu } \alpha \qquad b \qquad [m] \\ \text{Gegenkathete zu } \alpha \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ tan \alpha = \frac{a}{b}\\ \textbf{Gegeben:} \\ b=6\frac{1}{5}m \qquad a=3\frac{4}{5}m \qquad \\ \\ \textbf{Rechnung:} \\ tan \alpha = \frac{a}{b} \\ b=6\frac{1}{5}m\\ a=3\frac{4}{5}m\\ tan \alpha = \frac{3\frac{4}{5}m}{6\frac{1}{5}m}\\\\\alpha=31,5^{\circ} \\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline 6\frac{1}{5} m \\ \hline 62 dm \\ \hline 620 cm \\ \hline 6,2\cdot 10^{3} mm \\ \hline 6,2\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 3\frac{4}{5} m \\ \hline 38 dm \\ \hline 380 cm \\ \hline 3,8\cdot 10^{3} mm \\ \hline 3,8\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline alpha=\\ \hline 31,5 ° \\ \hline 1,89\cdot 10^{3} \text{'} \\ \hline 1,13\cdot 10^{5} \text{''} \\ \hline 35 gon \\ \hline 0,55 rad \\ \hline \end{array}$