Beispiel Nr: 01
$ \text{Gegeben:}\\\text{Höhe} \qquad c \qquad [m] \\ \text{Breite} \qquad b \qquad [m] \\ \text{Raumdiagonale} \qquad d \qquad [m] \\ \\ \text{Gesucht:} \\\text{Länge} \qquad a \qquad [m] \\ \\ a = \sqrt{d^{2} -b^{2} -c^{2} }\\ \textbf{Gegeben:} \\ c=4m \qquad b=6m \qquad d=10m \qquad \\ \\ \textbf{Rechnung:} \\ a = \sqrt{d^{2} -b^{2} -c^{2} } \\ c=4m\\ b=6m\\ d=10m\\ a = \sqrt{(10m)^{2} -(6m)^{2} -(4m)^{2} }\\\\a=6,93m \\\\\\ \tiny \begin{array}{|l|} \hline c=\\ \hline 4 m \\ \hline 40 dm \\ \hline 400 cm \\ \hline 4\cdot 10^{3} mm \\ \hline 4\cdot 10^{6} \mu m \\ \hline 0,004 km \\ \hline \end{array} \tiny \begin{array}{|l|} \hline b=\\ \hline 6 m \\ \hline 60 dm \\ \hline 600 cm \\ \hline 6\cdot 10^{3} mm \\ \hline 6\cdot 10^{6} \mu m \\ \hline 0,006 km \\ \hline \end{array} \tiny \begin{array}{|l|} \hline d=\\ \hline 10 m \\ \hline 100 dm \\ \hline 10^{3} cm \\ \hline 10^{4} mm \\ \hline 10^{7} \mu m \\ \hline 0,01 km \\ \hline \end{array} \tiny \begin{array}{|l|} \hline a=\\ \hline 6,93 m \\ \hline 69,3 dm \\ \hline 693 cm \\ \hline 6,93\cdot 10^{3} mm \\ \hline 6,93\cdot 10^{6} \mu m \\ \hline 0,00693 km \\ \hline \end{array}$