Geometrie-Dreieck-Gleichschenkliges rechtwinkliges Dreieck


  • $A = \frac{a\cdot b}{ 2}$
    1 2 3 4 5 6 7 8 9 10 11 12
    $a = \frac{A \cdot 2}{ b}$
    1 2 3 4 5 6 7 8 9 10 11 12
    $b = \frac{A \cdot 2}{ a}$
    1 2 3 4 5 6 7 8 9 10 11 12
    $a^{2} + b^{2}=c^{2}$
    $c =\sqrt{a^{2} + b^{2} }$
    1 2 3 4 5 6 7 8 9 10 11 12
    $a =\sqrt{c^{2} - b^{2} }$
    1 2 3 4 5 6 7 8 9 10
    $b =\sqrt{c^{2} - a^{2} }$
    1 2 3 4 5
    $h^{2} = p\cdot q$
    $h = \sqrt{p\cdot q}$
    1 2 3 4
    $q = \frac{h^{2} }{p}$
    1 2 3 4
    $p = \frac{h^{2} }{q}$
    1 2 3
    $a^{2} = c\cdot p \qquad b^{2} = c\cdot q $
    $a = \sqrt{c\cdot p}$
    1 2 3
    $c = \frac{a^{2} }{p}$
    1 2 3 4
    $p = \frac{a^{2} }{c}$
    1 2 3 4

Beispiel Nr: 02
$ \text{Gegeben:}\\\text{Gegenkathete zu }\alpha \qquad a \qquad [m] \\ \text{Hypotenuse} \qquad c \qquad [m] \\ \\ \text{Gesucht:} \\\text{Hypotenusenabschnitt} \qquad p \qquad [m] \\ \\ p = \frac{a^{2} }{c}\\ \textbf{Gegeben:} \\ a=6m \qquad c=4m \qquad \\ \\ \textbf{Rechnung:} \\ p = \frac{a^{2} }{c} \\ a=6m\\ c=4m\\ p = \frac{(6m)^{2} }{4m}\\\\p=9m \\\\\\ \small \begin{array}{|l|} \hline a=\\ \hline 6 m \\ \hline 60 dm \\ \hline 600 cm \\ \hline 6\cdot 10^{3} mm \\ \hline 6\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline 4 m \\ \hline 40 dm \\ \hline 400 cm \\ \hline 4\cdot 10^{3} mm \\ \hline 4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline p=\\ \hline 9 m \\ \hline 90 dm \\ \hline 900 cm \\ \hline 9\cdot 10^{3} mm \\ \hline 9\cdot 10^{6} \mu m \\ \hline \end{array}$