Geg: a=7,1 m, ß=34°, c=8,564m, alpha=56°, y=90° Wie errechne ich nun b?
$$\\
\begin{array}{rclr}
a&=&7,1~m\qquad &
\alpha = 56\ensurement{^{\circ}}\\
b&=& ~? ~m\qquad &
\beta = 34\ensurement{^{\circ}}\\
c&=&8,564~m\qquad&
\gamma = 90\ensurement{^{\circ}}\\
\end{array}$$
1. Möglichkeit:
$$\small{\text{$
\tan{(56\ensurement{^{\circ}})} =\dfrac{7,1}{b} \qquad b = \dfrac{7,1}{\tan{(56\ensurement{^{\circ}})} } = 4,789~m
$}}$$
2. Möglichkeit:
$$\small{\text{$
\cos{(56\ensurement{^{\circ}})} =\dfrac{b}{8,564} \qquad b = 8,564\cdot \cos{ (56\ensurement{^{\circ}}) } = 4,789~m
$}}$$
3. Möglichkeit:
$$\small{\text{$
\tan{(34\ensurement{^{\circ}})} =\dfrac{b}{7,1} \qquad b = 7,1\cdot \tan{ (34\ensurement{^{\circ}}) } = 4,789~m
$}}$$
4. Möglichkeit:
$$\small{\text{$
\sin{(34\ensurement{^{\circ}})} =\dfrac{b}{8,564} \qquad b = 8,564\cdot \sin{ (34\ensurement{^{\circ}}) } = 4,789~m $}}$$