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: 12
$ \text{Gegeben:}\\\text{Kathete} \qquad b \qquad [m] \\ \text{Fläche des Dreiecks} \qquad A \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Gegenkathete zu} \alpha \qquad a \qquad [m] \\ \\ a = \frac{A \cdot 2}{ b}\\ \textbf{Gegeben:} \\ b=\frac{3}{5}m \qquad A=1m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ a = \frac{A \cdot 2}{ b} \\ b=\frac{3}{5}m\\ A=1m^{2}\\ a = \frac{1m^{2} \cdot 2}{ \frac{3}{5}m}\\\\a=3\frac{1}{3}m \\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline \frac{3}{5} m \\ \hline 6 dm \\ \hline 60 cm \\ \hline 600 mm \\ \hline 6\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline 1 m^2 \\ \hline 100 dm^2 \\ \hline 10^{4} cm^2 \\ \hline 10^{6} mm^2 \\ \hline \frac{1}{100} a \\ \hline 0,0001 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 3\frac{1}{3} m \\ \hline 33\frac{1}{3} dm \\ \hline 333\frac{1}{3} cm \\ \hline 3333\frac{1}{3} mm \\ \hline 3333333\frac{1}{3} \mu m \\ \hline \end{array}$