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
$\text{Gegeben:}\\\text{Hypotenuse} \qquad c \qquad [m] \\ \text{Kathete} \qquad a \qquad \qquad [m] \\ \\ \text{Gesucht:} \\ \text{Kathete} \qquad b \qquad [m] \\ \\ b =\sqrt{c^{2} - a^{2} }\\ \textbf{Gegeben:} \\ c=15m \qquad a=12m \qquad \\ \\ \textbf{Rechnung:} \\ b =\sqrt{c^{2} - a^{2} } \\ c=15m\\ a=12m\\ b =\sqrt{(15m)^{2} - (12m)^{2} }\\\\b=9m \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline 15 m \\ \hline 150 dm \\ \hline 1,5\cdot 10^{3} cm \\ \hline 1,5\cdot 10^{4} mm \\ \hline 1,5\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 12 m \\ \hline 120 dm \\ \hline 1,2\cdot 10^{3} cm \\ \hline 1,2\cdot 10^{4} mm \\ \hline 1,2\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 9 m \\ \hline 90 dm \\ \hline 900 cm \\ \hline 9\cdot 10^{3} mm \\ \hline 9\cdot 10^{6} \mu m \\ \hline \end{array}$