Geometrie-Dreieck-Rechtwinkliges Dreieck


  • $A = \frac{a\cdot b}{ 2}$
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    $a = \frac{A \cdot 2}{ b}$
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    $b = \frac{A \cdot 2}{ a}$
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    $a^{2} + b^{2}=c^{2}$
    $c =\sqrt{a^{2} + b^{2} }$
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    $a =\sqrt{c^{2} - b^{2} }$
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    $b =\sqrt{c^{2} - a^{2} }$
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    $h^{2} = p\cdot q$
    $h = \sqrt{p\cdot q}$
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    $q = \frac{h^{2} }{p}$
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    $p = \frac{h^{2} }{q}$
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    $a^{2} = c\cdot p \qquad b^{2} = c\cdot q $
    $a = \sqrt{c\cdot p}$
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    $c = \frac{a^{2} }{p}$
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    $p = \frac{a^{2} }{c}$
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Beispiel Nr: 02
$ \text{Gegeben:}\\\text{Hypotenusenabschnitt} \qquad p \qquad [m] \\ \text{Höhe} \qquad h \qquad [m] \\ \\ \text{Gesucht:} \\\text{Hypotenusenabschnitt} \qquad q \qquad [m] \\ \\ q = \frac{h^{2} }{p}\\ \textbf{Gegeben:} \\ p=5m \qquad h=8m \qquad \\ \\ \textbf{Rechnung:} \\ q = \frac{h^{2} }{p} \\ p=5m\\ h=8m\\ q = \frac{(8m)^{2} }{5m}\\\\q=12\frac{4}{5}m \\\\\\ \small \begin{array}{|l|} \hline p=\\ \hline 5 m \\ \hline 50 dm \\ \hline 500 cm \\ \hline 5\cdot 10^{3} mm \\ \hline 5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline h=\\ \hline 8 m \\ \hline 80 dm \\ \hline 800 cm \\ \hline 8\cdot 10^{3} mm \\ \hline 8\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline q=\\ \hline 12\frac{4}{5} m \\ \hline 128 dm \\ \hline 1,28\cdot 10^{3} cm \\ \hline 1,28\cdot 10^{4} mm \\ \hline 1,28\cdot 10^{7} \mu m \\ \hline \end{array}$