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: 10
$ \text{Gegeben:}\\\text{Fläche des Dreiecks} \qquad A \qquad [m^{2}] \\ \text{Kathete} \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Ankathete zu } \alpha \qquad b \qquad [m] \\ \\ b = \frac{A \cdot 2}{ a}\\ \textbf{Gegeben:} \\ A_{d}=1\frac{1}{2}m^{2} \qquad a=\frac{1}{5}m \qquad \\ \\ \textbf{Rechnung:} \\ b = \frac{A \cdot 2}{ a} \\ A=1\frac{1}{2}m^{2}\\ a=\frac{1}{5}m\\ b = \frac{1\frac{1}{2}m^{2} \cdot 2}{ \frac{1}{5}m}\\\\b=15m \\\\\\ \small \begin{array}{|l|} \hline A=\\ \hline 1\frac{1}{2} m^2 \\ \hline 150 dm^2 \\ \hline 1,5\cdot 10^{4} cm^2 \\ \hline 1,5\cdot 10^{6} mm^2 \\ \hline 0,015 a \\ \hline 0,00015 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline \frac{1}{5} m \\ \hline 2 dm \\ \hline 20 cm \\ \hline 200 mm \\ \hline 2\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 15 m \\ \hline 150 dm \\ \hline 1,5\cdot 10^{3} cm \\ \hline 1,5\cdot 10^{4} mm \\ \hline 1,5\cdot 10^{7} \mu m \\ \hline \end{array}$