Formel for arealberegning

Sinusrelationen

\( \frac{a}{\sin \left( A \right)} = \frac{b}{\sin \left( B \right)} = \frac{c}{\sin \left( C \right)} = 2 \cdot R \)

\( \frac{\sin \left( A \right)}{a} = \frac{\sin \left( B \right)}{b} = \frac{\sin \left( C \right)}{c} = \frac{1}{2 \cdot R} \)

\( R = \text{radius i den omskrevne cirkel} \)

Cosinusrelationerne

\( a^2 = b^2 + c^2 - 2 \cdot b \cdot c \cdot \cos \left( A \right) \)

\( b^2 = a^2 + c^2 - 2 \cdot a \cdot c \cdot \cos \left( B \right) \)

\( c^2 = a^2 + b^2 - 2 \cdot a \cdot b \cdot \cos \left( C \right) \)

\( \cos \left( A \right) = \frac{b^2 + c^2 - a^2}{2 \cdot b \cdot c} \)

\( \cos \left( B \right) = \frac{a^2 + c^2 - b^2}{2 \cdot a \cdot c} \)

\( \cos \left( C \right) = \frac{a^2 + b^2 - c^2}{2 \cdot a \cdot b} \)

Tangensrelationerne

\( \tan \left( A \right) = \frac{\sin \left( B \right) \cdot a}{c - \cos \left( B \right) \cdot a} = \frac{\sin \left( C \right) \cdot a}{b - \cos \left( C \right) \cdot a} \)

\( \tan \left( B \right) = \frac{\sin \left( A \right) \cdot b}{c - \cos \left( A \right) \cdot b} = \frac{\sin \left( C \right) \cdot b}{a - \cos \left( C \right) \cdot b} \)

\( \tan \left( C \right) = \frac{\sin \left( A \right) \cdot c}{b - \cos \left( A \right) \cdot c} = \frac{\sin \left( B \right) \cdot c}{a - \cos \left( b \right) \cdot c} \)