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{Ankathete zu } \alpha \qquad b \qquad [m] \\ \\ \text{Gesucht:} \\\text{Hypotenuse} \qquad c \qquad [m] \\ \\ c = \frac{ b}{cos \alpha }\\ \textbf{Gegeben:} \\ \alpha=70^{\circ} \qquad b=34m \qquad \\ \\ \textbf{Rechnung:} \\ c = \frac{ b}{cos \alpha } \\ \alpha=70^{\circ}\\ b=34m\\ c = \frac{34m}{cos 70^{\circ} }\\\\c=99,4m \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 70 ° \\ \hline 4,2\cdot 10^{3} \text{'} \\ \hline 2,52\cdot 10^{5} \text{''} \\ \hline 77\frac{7}{9} gon \\ \hline 1,22 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 34 m \\ \hline 340 dm \\ \hline 3,4\cdot 10^{3} cm \\ \hline 3,4\cdot 10^{4} mm \\ \hline 3,4\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline 99,4 m \\ \hline 994 dm \\ \hline 9,94\cdot 10^{3} cm \\ \hline 9,94\cdot 10^{4} mm \\ \hline 9,94\cdot 10^{7} \mu m \\ \hline \end{array}$