geg: $a=7\text{cm}a=7\backslash ;\backslash text\{cm\}$; $b=18\text{cm}b=\; 18\backslash ;\backslash text\{cm\}$

ges: $\alpha ,\beta ,\backslash alpha,\backslash ;\backslash beta,\backslash ;$

Fertige am Besten zum Verständnis eine Skizze an.

Berechne $\alpha \backslash alpha$ mit Hilfe des Tangens.

$\tan \left(\alpha \right)=\frac{a}{b}\backslash tan\backslash left(\backslash alpha\backslash right)=\backslash frac\; ab$

Setz die Werte ein und berechne $\alpha \backslash alpha$ mit Hilfe des Taschenrechners.

$\tan (\alpha )=\frac{7\text{cm}}{18\text{cm}}\backslash tan(\backslash alpha)\; =\; \backslash frac\; \{7\backslash text\{cm\}\}\{18\backslash text\{cm\}\}$

$\alpha ={\mathrm{21,3}}^{\circ }\backslash alpha=21\{,\}3^\backslash circ$

Berechne $\beta \backslash beta$. $\alpha \backslash alpha$ und $\beta \backslash beta$ sind zusammen 90° also gilt für $\beta \backslash beta$:

$\beta ={90}^{\circ }-{\mathrm{21,3}}^{\circ }={\mathrm{68,7}}^{\circ }\backslash beta=90^\backslash circ-21\{,\}3^\backslash circ=68\{,\}7^\backslash circ$

geg: $\alpha ={\mathrm{21,3}}^{\circ };\beta ={\mathrm{68,7}}^{\circ }\backslash alpha=21\{,\}3^\backslash circ;\backslash ;\backslash beta=68\{,\}7^\backslash circ$

ges: $\gamma ,\delta \backslash gamma,\backslash ;\backslash delta$

Fertige am Besten zum Verständnis eine Skizze an.

$\delta \backslash delta$ ist 2 $\alpha \backslash alpha$ , weil $\delta \backslash delta$ $++$ $\gamma \backslash gamma$ $==$180° und $\gamma \backslash gamma$ $+2+2$ $\alpha \backslash alpha$ $==$180° im gleichschenklichen Dreieck gilt.

$\Rightarrow \backslash Rightarrow$ $\delta \backslash delta$ + $\gamma \backslash gamma$ $==$ $\gamma \backslash gamma$ $+2+2$ $\alpha \backslash alpha$

$\Rightarrow \backslash Rightarrow$ $\delta \backslash delta$ $==$$22$ $\alpha \backslash alpha$

$\delta =2\cdot {\mathrm{21,3}}^{\circ }={\mathrm{42,6}}^{\circ }\backslash delta=2\backslash cdot21\{,\}3^\backslash circ=42\{,\}6^\backslash circ$

$\gamma \backslash gamma$ und $\delta \backslash delta$ bilden zusammen 180°.

$\gamma ={180}^{\circ }-{\mathrm{42,6}}^{\circ }={\mathrm{137,4}}^{\circ }\backslash gamma=180^\{\backslash circ\}-42\{,\}6^\{\backslash circ\}=137\{,\}4^\{\backslash circ\}$