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: 03
$\text{Gegeben:}\\\text{Hypotenusenabschnitt} \qquad p \qquad [m] \\ \text{Hypotenuse} \qquad c \qquad [m] \\ \\ \text{Gesucht:} \\\text{Gegenkathete zu } \alpha \qquad a \qquad [m] \\ \\ a = \sqrt{c\cdot p}\\ \textbf{Gegeben:} \\ p=1m \qquad c=\frac{1}{9}m \qquad \\ \\ \textbf{Rechnung:} \\ a = \sqrt{c\cdot p} \\ p=1m\\ c=\frac{1}{9}m\\ a = \sqrt{\frac{1}{9}m\cdot 1m}\\\\a=\frac{1}{3}m \\\\\\ \small \begin{array}{|l|} \hline p=\\ \hline 1 m \\ \hline 10 dm \\ \hline 100 cm \\ \hline 10^{3} mm \\ \hline 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline \frac{1}{9} m \\ \hline 1\frac{1}{9} dm \\ \hline 11\frac{1}{9} cm \\ \hline 111\frac{1}{9} mm \\ \hline 111111\frac{1}{9} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline \frac{1}{3} m \\ \hline 3\frac{1}{3} dm \\ \hline 33\frac{1}{3} cm \\ \hline 333\frac{1}{3} mm \\ \hline 333333\frac{1}{3} \mu m \\ \hline \end{array}$