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: 06
$\begin{array}{l} \text{Gegeben:}\\\text{Fläche des Dreiecks} \qquad A \qquad [m^{2}] \\ \text{Kathete} \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Ankathete zu } \alpha \qquad b \qquad [m] \\ \\ b = \frac{A \cdot 2}{ a}\\ \textbf{Gegeben:} \\ A_{d}=120m^{2} \qquad a=80m \qquad \\ \\ \textbf{Rechnung:} \\ b = \frac{A \cdot 2}{ a} \\ A=120m^{2}\\ a=80m\\ b = \frac{120m^{2} \cdot 2}{ 80m}\\\\b=3m \\\\\\ \small \begin{array}{|l|} \hline A=\\ \hline 120 m^2 \\ \hline 1,2\cdot 10^{4} dm^2 \\ \hline 1,2\cdot 10^{6} cm^2 \\ \hline 1,2\cdot 10^{8} mm^2 \\ \hline 1\frac{1}{5} a \\ \hline 0,012 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 80 m \\ \hline 800 dm \\ \hline 8\cdot 10^{3} cm \\ \hline 8\cdot 10^{4} mm \\ \hline 8\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 3 m \\ \hline 30 dm \\ \hline 300 cm \\ \hline 3\cdot 10^{3} mm \\ \hline 3\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$