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{Hypotenuse} \qquad c \qquad [m] \\ \\ \text{Gesucht:} \\\text{Gegenkathete zu } \alpha \qquad a \qquad [m] \\ \\ a = \sqrt{c\cdot p}\\ \textbf{Gegeben:} \\ p=7m \qquad c=2m \qquad \\ \\ \textbf{Rechnung:} \\ a = \sqrt{c\cdot p} \\ p=7m\\ c=2m\\ a = \sqrt{2m\cdot 7m}\\\\a=3,74m \\\\\\ \small \begin{array}{|l|} \hline p=\\ \hline 7 m \\ \hline 70 dm \\ \hline 700 cm \\ \hline 7\cdot 10^{3} mm \\ \hline 7\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline 2 m \\ \hline 20 dm \\ \hline 200 cm \\ \hline 2\cdot 10^{3} mm \\ \hline 2\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 3,74 m \\ \hline 37,4 dm \\ \hline 374 cm \\ \hline 3,74\cdot 10^{3} mm \\ \hline 3,74\cdot 10^{6} \mu m \\ \hline \end{array}$