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$ a = \sqrt{b^{2} +c^{2} -2\cdot b\cdot c\cdot cos\alpha } $
$ cos\alpha = \frac{b^{2} +c^{2} -a^{2} }{2\cdot b\cdot c} $
Geometrie-Trigonometrie-Kosinussatz
$ a^2 = b^{2} +c^{2} -2\cdot b\cdot c\cdot cos\alpha $
$a = \sqrt{b^{2} +c^{2} -2\cdot b\cdot c\cdot cos\alpha }$
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$cos\alpha = \frac{b^{2} +c^{2} -a^{2} }{2\cdot b\cdot c}$
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Beispiel Nr: 01
$\begin{array}{l}
\text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\
\text{Länge der Seite} \qquad c \qquad [m] \\
\text{Länge der Seite} \qquad b \qquad [m] \\
\\ \text{Gesucht:} \\\text{Länge der Seite} \qquad a \qquad [m] \\
\\ a = \sqrt{b^{2} +c^{2} -2\cdot b\cdot c\cdot cos\alpha }\\ \textbf{Gegeben:} \\ \alpha=60^{\circ} \qquad c=7m \qquad b=7m \qquad \\ \\ \textbf{Rechnung:} \\
a = \sqrt{b^{2} +c^{2} -2\cdot b\cdot c\cdot cos\alpha } \\
\alpha=60^{\circ}\\
c=7m\\
b=7m\\
a = \sqrt{(7m)^{2} +(7m)^{2} -2\cdot 7m \cdot 7m\cdot cos60^{\circ} }\\\\a=7m
\\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 60 ° \\ \hline 3,6\cdot 10^{3} \text{'} \\ \hline 2,16\cdot 10^{5} \text{''} \\ \hline 66\frac{2}{3} gon \\ \hline 1,05 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline 7 m \\ \hline 70 dm \\ \hline 700 cm \\ \hline 7\cdot 10^{3} mm \\ \hline 7\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 7 m \\ \hline 70 dm \\ \hline 700 cm \\ \hline 7\cdot 10^{3} mm \\ \hline 7\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 7 m \\ \hline 70 dm \\ \hline 700 cm \\ \hline 7\cdot 10^{3} mm \\ \hline 7\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$