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: 01
$ \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=6m \qquad h=4m \qquad \\ \\ \textbf{Rechnung:} \\ q = \frac{h^{2} }{p} \\ p=6m\\ h=4m\\ q = \frac{(4m)^{2} }{6m}\\\\q=2\frac{2}{3}m \\\\\\ \small \begin{array}{|l|} \hline p=\\ \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 h=\\ \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 q=\\ \hline 2\frac{2}{3} m \\ \hline 26\frac{2}{3} dm \\ \hline 266\frac{2}{3} cm \\ \hline 2666\frac{2}{3} mm \\ \hline 2666666\frac{2}{3} \mu m \\ \hline \end{array}$