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{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \text{Gegenkathete zu } \alpha \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Ankathete zu } \alpha \qquad b \qquad [m] \\ \\ b = \frac{ a}{tan\alpha }\\ \textbf{Gegeben:} \\ \alpha=60^{\circ} \qquad a=1\frac{1}{5}m \qquad \\ \\ \textbf{Rechnung:} \\ b = \frac{ a}{tan\alpha } \\ \alpha=60^{\circ}\\ a=1\frac{1}{5}m\\ b = \frac{ 1\frac{1}{5}m}{tan60^{\circ} }\\\\b=0,693m \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 60 ° \\ \hline 3,6\cdot 10^{3} \text{'} \\ \hline 2,16\cdot 10^{5} \text{''} \\ \hline 66\frac{2}{3} gon \\ \hline 1,05 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 1\frac{1}{5} m \\ \hline 12 dm \\ \hline 120 cm \\ \hline 1,2\cdot 10^{3} mm \\ \hline 1,2\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 0,693 m \\ \hline 6,93 dm \\ \hline 69,3 cm \\ \hline 693 mm \\ \hline 6,93\cdot 10^{5} \mu m \\ \hline \end{array}$