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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-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: 11
$\begin{array}{l}
\text{Gegeben:}\\\text{Kathete} \qquad b \qquad [m] \\
\text{Fläche des Dreiecks} \qquad A \qquad [m^{2}] \\
\\ \text{Gesucht:} \\\text{Gegenkathete zu} \alpha \qquad a \qquad [m] \\
\\ a = \frac{A \cdot 2}{ b}\\ \textbf{Gegeben:} \\ b=1\frac{1}{5}m \qquad A=1\frac{1}{2}m^{2} \qquad \\ \\ \textbf{Rechnung:} \\
a = \frac{A \cdot 2}{ b} \\
b=1\frac{1}{5}m\\
A=1\frac{1}{2}m^{2}\\
a = \frac{1\frac{1}{2}m^{2} \cdot 2}{ 1\frac{1}{5}m}\\\\a=2\frac{1}{2}m
\\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline 1\frac{1}{5} m \\ \hline 12 dm \\ \hline 120 cm \\ \hline 1,2\cdot 10^{3} mm \\ \hline 1,2\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline 1\frac{1}{2} m^2 \\ \hline 150 dm^2 \\ \hline 1,5\cdot 10^{4} cm^2 \\ \hline 1,5\cdot 10^{6} mm^2 \\ \hline 0,015 a \\ \hline 0,00015 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 2\frac{1}{2} m \\ \hline 25 dm \\ \hline 250 cm \\ \hline 2,5\cdot 10^{3} mm \\ \hline 2,5\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$