Die $\text{t}\ddot{\text{u}}\text{rkisfarbene Strecke}\backslash textcolor\{009999\}\{\backslash text\{türkisfarbene\; Strecke\}\; \}$ nennst Du $xx$.

Berechne $xx$ mit dem 1. Strahlensatz:

Es gilt:

${\displaystyle \frac{x}{\mathrm{1,9}}}={\displaystyle \frac{\mathrm{6,4}}{\mathrm{2,4}}}\Rightarrow x={\displaystyle \frac{\mathrm{1,9}\cdot \mathrm{6,4}}{\mathrm{2,4}}}\approx \mathrm{5,1}\backslash dfrac\{x\}\{1\{,\}9\}=\backslash dfrac\{6\{,\}4\}\{2\{,\}4\}\backslash ;\backslash Rightarrow\backslash ;x=\backslash dfrac\{1\{,\}9\backslash cdot\; 6\{,\}4\}\{2\{,\}4\}\backslash approx5\{,\}1$

Die $\text{orangefarbene Strecke}\backslash textcolor\{ff6600\}\{\backslash text\{orangefarbene\; Strecke\}\; \}$ nennst Du $yy$.

Berechne $yy$ mit dem 2. Strahlensatz:

Es gilt:

${\displaystyle \frac{y}{\mathrm{6,4}+\mathrm{2,4}}}={\displaystyle \frac{4}{\mathrm{6,4}}}\Rightarrow y={\displaystyle \frac{(\mathrm{6,4}+\mathrm{2,4})\cdot 4}{\mathrm{6,4}}}={\displaystyle \frac{\mathrm{8,8}\cdot 4}{\mathrm{6,4}}}=\mathrm{5,5}\backslash dfrac\{y\}\{6\{,\}4+2\{,\}4\}=\backslash dfrac\{4\}\{6\{,\}4\}\backslash ;\backslash Rightarrow\backslash ;y=\backslash dfrac\{(6\{,\}4+2\{,\}4)\backslash cdot\; 4\}\{6\{,\}4\}=\backslash dfrac\{8\{,\}8\backslash cdot\; 4\}\{6\{,\}4\}=5\{,\}5$