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 a \qquad [m] \\ \text{Kathete} \qquad b \qquad [m] \\ \\ \text{Gesucht:} \\\text{Hypotenuse} \qquad c \qquad [m] \\ \\ c =\sqrt{a^{2} + b^{2} }\\ \textbf{Gegeben:} \\ a=120m \qquad b=80m \qquad \\ \\ \textbf{Rechnung:} \\ c =\sqrt{a^{2} + b^{2} } \\ a=120m\\ b=80m\\ c =\sqrt{(120m)^{2} + (80m)^{2} }\\\\c=144m \\\\\\ \small \begin{array}{|l|} \hline a=\\ \hline 120 m \\ \hline 1,2\cdot 10^{3} dm \\ \hline 1,2\cdot 10^{4} cm \\ \hline 1,2\cdot 10^{5} mm \\ \hline 1,2\cdot 10^{8} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 80 m \\ \hline 800 dm \\ \hline 8\cdot 10^{3} cm \\ \hline 8\cdot 10^{4} mm \\ \hline 8\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline 144 m \\ \hline 1,44\cdot 10^{3} dm \\ \hline 1,44\cdot 10^{4} cm \\ \hline 1,44\cdot 10^{5} mm \\ \hline 1,44\cdot 10^{8} \mu m \\ \hline \end{array}$