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: 05
$ \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=\frac{3}{10}m \qquad a=\frac{1}{10}m \\ \\ \textbf{Rechnung:} \\ sin \alpha = \frac{a}{c} \\ c=\frac{3}{10}m\\ a=\frac{1}{10}m\\ sin \alpha = \frac{\frac{1}{10}m}{\frac{3}{10}m}\\ \\ \alpha=19,5^{\circ} \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline \frac{3}{10} m \\ \hline 3 dm \\ \hline 30 cm \\ \hline 300 mm \\ \hline 3\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline \frac{1}{10} m \\ \hline 1 dm \\ \hline 10 cm \\ \hline 100 mm \\ \hline 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline alpha=\\ \hline 19,5 ° \\ \hline 1,17\cdot 10^{3} \text{'} \\ \hline 7,01\cdot 10^{4} \text{''} \\ \hline 21,6 gon \\ \hline 0,34 rad \\ \hline \end{array}$