$\begin{array}{c}a=\tan \left(\alpha \right)\cdot h\\ a=\tan \left({65}^{\circ }\right)\cdot 8\mathrm{c}\mathrm{m}\\ a=\mathrm{17,16}\mathrm{c}\mathrm{m}\\ \\ a+b=\tan \left(\beta \right)\cdot h\\ a+b=\tan \left({80}^{\circ }\right)\cdot 8\mathrm{c}\mathrm{m}\\ a+b=\mathrm{45,37}\mathrm{c}\mathrm{m}\end{array}\backslash def\backslash arraystretch\{1.25\}\; \backslash begin\{array\}\{l\}a=\backslash tan\backslash left(\backslash alpha\backslash right)\backslash cdot\; h\backslash \backslash a=\backslash tan\backslash left(65^\backslash circ\backslash right)\backslash cdot8\backslash ,\backslash mathrm\{cm\}\backslash \backslash a=17\{,\}16\backslash ,\backslash mathrm\{cm\}\backslash \backslash \backslash \backslash a+b=\backslash tan\backslash left(\backslash beta\backslash right)\backslash cdot\; h\backslash \backslash a+b=\backslash tan\backslash left(80^\backslash circ\backslash right)\backslash cdot8\backslash ,\backslash mathrm\{cm\}\backslash \backslash a+b=45\{,\}37\backslash ,\backslash mathrm\{cm\}\backslash end\{array\}$

Damit ist $b=\mathrm{45,37}\text{ cm }-\mathrm{17,16}\text{ cm }=\mathrm{28,21}\text{ cm}b=45\{,\}37\backslash text\{\backslash \; cm\; \}-17\{,\}16\backslash text\{\backslash \; cm\backslash \; \}=28\{,\}21\backslash \; \backslash text\{cm\}$.