Geometrie-Dreieck-Rechtwinkliges Dreieck

• $A = \frac{a\cdot b}{ 2}$
1 2 3 4 5 6 7 8 9 10 11 12
$a = \frac{A \cdot 2}{ b}$
1 2 3 4 5 6 7 8 9 10 11 12
$b = \frac{A \cdot 2}{ a}$
1 2 3 4 5 6 7 8 9 10 11 12
$a^{2} + b^{2}=c^{2}$
$c =\sqrt{a^{2} + b^{2} }$
1 2 3 4 5 6 7 8 9 10 11 12
$a =\sqrt{c^{2} - b^{2} }$
1 2 3 4 5 6 7 8 9 10
$b =\sqrt{c^{2} - a^{2} }$
1 2 3 4 5
$h^{2} = p\cdot q$
$h = \sqrt{p\cdot q}$
1 2 3 4
$q = \frac{h^{2} }{p}$
1 2 3 4
$p = \frac{h^{2} }{q}$
1 2 3
$a^{2} = c\cdot p \qquad b^{2} = c\cdot q$
$a = \sqrt{c\cdot p}$
1 2 3
$c = \frac{a^{2} }{p}$
1 2 3 4
$p = \frac{a^{2} }{c}$
1 2 3 4

Beispiel Nr: 12
$\text{Gegeben:}\\\text{Fläche des Dreiecks} \qquad A \qquad [m^{2}] \\ \text{Kathete} \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Ankathete zu } \alpha \qquad b \qquad [m] \\ \\ b = \frac{A \cdot 2}{ a}\\ \textbf{Gegeben:} \\ A_{d}=\frac{3}{5}m^{2} \qquad a=1m \qquad \\ \\ \textbf{Rechnung:} \\ b = \frac{A \cdot 2}{ a} \\ A=\frac{3}{5}m^{2}\\ a=1m\\ b = \frac{\frac{3}{5}m^{2} \cdot 2}{ 1m}\\\\b=1\frac{1}{5}m \\\\\\ \small \begin{array}{|l|} \hline A=\\ \hline \frac{3}{5} m^2 \\ \hline 60 dm^2 \\ \hline 6\cdot 10^{3} cm^2 \\ \hline 6\cdot 10^{5} mm^2 \\ \hline 0,006 a \\ \hline 6\cdot 10^{-5} ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 1 m \\ \hline 10 dm \\ \hline 100 cm \\ \hline 10^{3} mm \\ \hline 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 1\frac{1}{5} m \\ \hline 12 dm \\ \hline 120 cm \\ \hline 1,2\cdot 10^{3} mm \\ \hline 1,2\cdot 10^{6} \mu m \\ \hline \end{array}$