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 a \qquad \qquad [m] \\ \\ \text{Gesucht:} \\ \text{Kathete} \qquad b \qquad [m] \\ \\ b =\sqrt{c^{2} - a^{2} }\\ \textbf{Gegeben:} \\ c=\frac{1}{2}m \qquad a=\frac{2}{5}m \qquad \\ \\ \textbf{Rechnung:} \\ b =\sqrt{c^{2} - a^{2} } \\ c=\frac{1}{2}m\\ a=\frac{2}{5}m\\ b =\sqrt{(\frac{1}{2}m)^{2} - (\frac{2}{5}m)^{2} }\\\\b=\frac{3}{10}m \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline \frac{1}{2} m \\ \hline 5 dm \\ \hline 50 cm \\ \hline 500 mm \\ \hline 5\cdot 10^{5} \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 b=\\ \hline \frac{3}{10} m \\ \hline 3 dm \\ \hline 30 cm \\ \hline 300 mm \\ \hline 3\cdot 10^{5} \mu m \\ \hline \end{array}$