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: 06
$ \text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \text{Hypotenuse} \qquad c \qquad [m] \\ \\ \text{Gesucht:} \\\text{Ankathete zu } \alpha \qquad b \qquad [m] \\ \\ b = cos \alpha \cdot c\\ \textbf{Gegeben:} \\ \alpha=20^{\circ} \qquad c=6\frac{1}{2}m \qquad \\ \\ \textbf{Rechnung:} \\ b = cos \alpha \cdot c \\ \alpha=20^{\circ}\\ c=6\frac{1}{2}m\\ b = cos 20^{\circ} \cdot 6\frac{1}{2}m\\\\b=6,11m \\\\\\ \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 c=\\ \hline 6\frac{1}{2} m \\ \hline 65 dm \\ \hline 650 cm \\ \hline 6,5\cdot 10^{3} mm \\ \hline 6,5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 6,11 m \\ \hline 61,1 dm \\ \hline 611 cm \\ \hline 6,11\cdot 10^{3} mm \\ \hline 6,11\cdot 10^{6} \mu m \\ \hline \end{array}$