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{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}=\frac{1}{3}m^{2} \qquad a=\frac{3}{4}m \qquad \\ \\ \textbf{Rechnung:} \\ b = \frac{A \cdot 2}{ a} \\ A=\frac{1}{3}m^{2}\\ a=\frac{3}{4}m\\ b = \frac{\frac{1}{3}m^{2} \cdot 2}{ \frac{3}{4}m}\\\\b=\frac{8}{9}m \\\\\\ \small \begin{array}{|l|} \hline A=\\ \hline \frac{1}{3} m^2 \\ \hline 33\frac{1}{3} dm^2 \\ \hline 3333\frac{1}{3} cm^2 \\ \hline 333333\frac{1}{3} mm^2 \\ \hline 0,00333 a \\ \hline 3,33\cdot 10^{-5} ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline \frac{3}{4} m \\ \hline 7\frac{1}{2} dm \\ \hline 75 cm \\ \hline 750 mm \\ \hline 7,5\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline \frac{8}{9} m \\ \hline 8\frac{8}{9} dm \\ \hline 88\frac{8}{9} cm \\ \hline 888\frac{8}{9} mm \\ \hline 888888\frac{8}{9} \mu m \\ \hline \end{array}$