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: 02
$ \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=20^{\circ} \qquad a=8m \\ \\ \textbf{Rechnung:} \\ c = \frac{ a}{sin\alpha } \\ \alpha=20^{\circ}\\ a=8m\\ c = \frac{8m}{sin20^{\circ} }\\\\c=23,4m \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 20 ° \\ \hline 1,2\cdot 10^{3} \text{'} \\ \hline 7,2\cdot 10^{4} \text{''} \\ \hline 22\frac{2}{9} gon \\ \hline 0,349 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 8 m \\ \hline 80 dm \\ \hline 800 cm \\ \hline 8\cdot 10^{3} mm \\ \hline 8\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline 23,4 m \\ \hline 234 dm \\ \hline 2,34\cdot 10^{3} cm \\ \hline 2,34\cdot 10^{4} mm \\ \hline 2,34\cdot 10^{7} \mu m \\ \hline \end{array}$