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{Kathete} \qquad b \qquad [m] \\ \text{Fläche des Dreiecks} \qquad A \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Gegenkathete zu} \alpha \qquad a \qquad [m] \\ \\ a = \frac{A \cdot 2}{ b}\\ \textbf{Gegeben:} \\ b=\frac{1}{3}m \qquad A=\frac{3}{4}m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ a = \frac{A \cdot 2}{ b} \\ b=\frac{1}{3}m\\ A=\frac{3}{4}m^{2}\\ a = \frac{\frac{3}{4}m^{2} \cdot 2}{ \frac{1}{3}m}\\\\a=4\frac{1}{2}m \\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline \frac{1}{3} m \\ \hline 3\frac{1}{3} dm \\ \hline 33\frac{1}{3} cm \\ \hline 333\frac{1}{3} mm \\ \hline 333333\frac{1}{3} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline \frac{3}{4} m^2 \\ \hline 75 dm^2 \\ \hline 7,5\cdot 10^{3} cm^2 \\ \hline 7,5\cdot 10^{5} mm^2 \\ \hline 0,0075 a \\ \hline 7,5\cdot 10^{-5} ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 4\frac{1}{2} m \\ \hline 45 dm \\ \hline 450 cm \\ \hline 4,5\cdot 10^{3} mm \\ \hline 4,5\cdot 10^{6} \mu m \\ \hline \end{array}$