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$ A = \frac{a\cdot b}{ 2} $
$ a = \frac{A \cdot 2}{ b} $
$ b = \frac{A \cdot 2}{ a} $
$ c =\sqrt{a^{2} + b^{2} } $
$ a =\sqrt{c^{2} - b^{2} } $
$ b =\sqrt{c^{2} - a^{2} } $
$ h = \sqrt{p\cdot q} $
$ q = \frac{h^{2} }{p} $
$ p = \frac{h^{2} }{q} $
$ a = \sqrt{c\cdot p} $
$ c = \frac{a^{2} }{p} $
$ p = \frac{a^{2} }{c} $
Geometrie-Dreieck-Gleichschenkliges 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: 09
$\begin{array}{l}
\text{Gegeben:}\\\text{Fläche des Dreiecks} \qquad A \qquad [m^{2}] \\
\text{Kathete} \qquad a \qquad [m] \\
\\ \text{Gesucht:} \\\text{Ankathete zu } \alpha \qquad b \qquad [m] \\
\\ b = \frac{A \cdot 2}{ a}\\ \textbf{Gegeben:} \\ A_{d}=\frac{1}{3}m^{2} \qquad a=1m \qquad \\ \\ \textbf{Rechnung:} \\
b = \frac{A \cdot 2}{ a} \\
A=\frac{1}{3}m^{2}\\
a=1m\\
b = \frac{\frac{1}{3}m^{2} \cdot 2}{ 1m}\\\\b=\frac{2}{3}m
\\\\\\ \small \begin{array}{|l|} \hline A=\\ \hline \frac{1}{3} m^2 \\ \hline 33\frac{1}{3} dm^2 \\ \hline 3333\frac{1}{3} cm^2 \\ \hline 333333\frac{1}{3} mm^2 \\ \hline 0,00333 a \\ \hline 3,33\cdot 10^{-5} ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 1 m \\ \hline 10 dm \\ \hline 100 cm \\ \hline 10^{3} mm \\ \hline 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline \frac{2}{3} m \\ \hline 6\frac{2}{3} dm \\ \hline 66\frac{2}{3} cm \\ \hline 666\frac{2}{3} mm \\ \hline 666666\frac{2}{3} \mu m \\ \hline \end{array} \end{array}$