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: 05
$ \text{Gegeben:}\\\text{Hypotenuse} \qquad c \qquad [m] \\ \text{Kathete}\qquad b \qquad [m] \\ \\ \text{Gesucht:} \\ \text{Kathete} \qquad a \qquad [m] \\ \\ a =\sqrt{c^{2} - b^{2} }\\ \textbf{Gegeben:} \\ c=25m \qquad b=24m \qquad \\ \\ \textbf{Rechnung:} \\ a =\sqrt{c^{2} - b^{2} } \\ c=25m\\ b=24m\\ a =\sqrt{(25m)^{2} - (24m)^{2} }\\\\a=7m \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline 25 m \\ \hline 250 dm \\ \hline 2,5\cdot 10^{3} cm \\ \hline 2,5\cdot 10^{4} mm \\ \hline 2,5\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 24 m \\ \hline 240 dm \\ \hline 2,4\cdot 10^{3} cm \\ \hline 2,4\cdot 10^{4} mm \\ \hline 2,4\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \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}$