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: 08
$ \text{Gegeben:}\\\text{Kathete} \qquad b \qquad [m] \\ \text{Kathete} \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Fläche} \qquad A \qquad [m^{2}] \\ \\ A = \frac{a\cdot b}{ 2}\\ \textbf{Gegeben:} \\ b=0,002m \qquad a=\frac{2}{5}m \qquad \\ \\ \textbf{Rechnung:} \\ A = \frac{a\cdot b}{ 2} \\ b=0,002m\\ a=\frac{2}{5}m\\ A = \frac{\frac{2}{5}m\cdot 0,002m}{ 2}\\\\A=0,0004m^{2} \\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline 0,002 m \\ \hline \frac{1}{50} dm \\ \hline \frac{1}{5} cm \\ \hline 2 mm \\ \hline 2\cdot 10^{3} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline \frac{2}{5} m \\ \hline 4 dm \\ \hline 40 cm \\ \hline 400 mm \\ \hline 4\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline 0,0004 m^2 \\ \hline \frac{1}{25} dm^2 \\ \hline 4 cm^2 \\ \hline 400 mm^2 \\ \hline 4\cdot 10^{-6} a \\ \hline 4\cdot 10^{-8} ha \\ \hline \end{array}$