$\mathrm{3,10}\text{ cm}-\mathrm{2,20}\text{ cm}=90\text{ cm}3\{,\}10\backslash cm-2\{,\}20\backslash cm=90\backslash cm$

$c^2=a^2+b^{2}c^2=a^2+b^2$

$x^2={90}^2+{430}^2=8100+184900=193000x^2=90^2+430^2=8100+184900=193000$

$x=\sqrt{193000}x=\backslash sqrt\{193000\}$ $=\mathrm{439,31765273}=439\{,\}31765273\backslash$

Die Länge x des Dachbalkens beträgt ca. $\mathrm{4,39}\text{ m}4\{,\}39\backslash m$.

${\displaystyle \sin (\alpha )=\frac{\text{Gegenkathete}}{\text{Hypotenuse}}}\backslash \; \backslash displaystyle\backslash sin(\backslash alpha)=\backslash dfrac\{\backslash text\{Gegenkathete\}\}\{\backslash text\{Hypotenuse\}\}$

${\displaystyle \sin (\alpha )=\frac{90}{439}\approx \mathrm{0,205}}\backslash \; \backslash displaystyle\backslash sin(\backslash alpha)=\backslash frac\{90\}\{439\}\backslash approx\; 0\{,\}205$

$\alpha \approx \backslash alpha\backslash approx$ 11,82°

$\beta +53\mathrm{°}+90\mathrm{°}=180\mathrm{°}\backslash beta+53°+90°=180°$

$\beta =37\mathrm{°}\backslash beta=37°$

${\displaystyle \cos (\beta )=\frac{\text{Ankathete}}{\text{Hypotenuse}}}\backslash displaystyle\backslash cos(\backslash beta)=\backslash frac\{\backslash text\{Ankathete\}\}\{\backslash text\{Hypotenuse\}\}$

${\displaystyle \cos (37\mathrm{°})=\frac{430}{s}}\backslash displaystyle\backslash cos(37°)=\backslash frac\{430\}\{s\}$

${\displaystyle s=\frac{430}{\mathrm{0,7986...}}}\backslash displaystyle\; s=\backslash frac\{430\}\{0\{,\}7986...\}$

$s\approx \mathrm{538,42}s\backslash approx538\{,\}42$

Die Solaranlage hat ungefähr die Länge $\mathrm{538,42}\text{ cm}538\{,\}42\; \backslash cm$.