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: 03
$ \text{Gegeben:}\\\text{Gegenkathete zu }\alpha \qquad a \qquad [m] \\ \text{Hypotenuse} \qquad c \qquad [m] \\ \\ \text{Gesucht:} \\\text{Hypotenusenabschnitt} \qquad p \qquad [m] \\ \\ p = \frac{a^{2} }{c}\\ \textbf{Gegeben:} \\ a=3m \qquad c=4m \qquad \\ \\ \textbf{Rechnung:} \\ p = \frac{a^{2} }{c} \\ a=3m\\ c=4m\\ p = \frac{(3m)^{2} }{4m}\\\\p=2\frac{1}{4}m \\\\\\ \small \begin{array}{|l|} \hline a=\\ \hline 3 m \\ \hline 30 dm \\ \hline 300 cm \\ \hline 3\cdot 10^{3} mm \\ \hline 3\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \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 p=\\ \hline 2\frac{1}{4} m \\ \hline 22\frac{1}{2} dm \\ \hline 225 cm \\ \hline 2,25\cdot 10^{3} mm \\ \hline 2,25\cdot 10^{6} \mu m \\ \hline \end{array}$