Beispiel Nr: 04
$ \text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \text{Ankathete zu } \alpha \qquad b \qquad [m] \\ \\ \text{Gesucht:} \\\text{Gegenkathete zu } \alpha \qquad a \qquad [m] \\ \\ a = tan \alpha \cdot b\\ \textbf{Gegeben:} \\ \alpha=30^{\circ} \qquad b=4\frac{1}{2}m \qquad \\ \\ \textbf{Rechnung:} \\ a = tan \alpha \cdot b \\ \alpha=30^{\circ}\\ b=4\frac{1}{2}m\\ a = tan 30^{\circ} \cdot 4\frac{1}{2}m\\\\a=2,6m \\\\\\ \tiny \begin{array}{|l|} \hline alpha=\\ \hline 30 ° \\ \hline 1,8\cdot 10^{3} \text{'} \\ \hline 1,08\cdot 10^{5} \text{''} \\ \hline 33,3 gon \\ \hline 0,524 rad \\ \hline 0,000524 mrad \\ \hline \end{array} \tiny \begin{array}{|l|} \hline b=\\ \hline 4,5 m \\ \hline 45 dm \\ \hline 450 cm \\ \hline 4,5\cdot 10^{3} mm \\ \hline 4,5\cdot 10^{6} \mu m \\ \hline 0,0045 km \\ \hline \end{array} \tiny \begin{array}{|l|} \hline a=\\ \hline 2,6 m \\ \hline 26 dm \\ \hline 260 cm \\ \hline 2,6\cdot 10^{3} mm \\ \hline 2,6\cdot 10^{6} \mu m \\ \hline 0,0026 km \\ \hline \end{array}$