26Obliczam α
[tex]a^2=b^2+c^2-2ab cos\alpha\\\\9^2=5^2+11^2-2\cdot5\cdot11 cos\alpha\\\\81=25+121-110cos\alpha\\\\110cos\alpha=25+121-81\\\\110cos\alpha=65\ \ \ |:110\\\\cos\alpha=\frac{65}{110}\\\\cos\alpha\approx0,5909\\\\\alpha\approx53,8^o[/tex]
Obliczam β
[tex]b^2=a^2+c^2-2ac cos\beta\\\\5^2=9^2+11^2-2\cdot9\cdot11 cos\beta\\\\25=81+121-198cos\beta\\\\198cos\beta=81+121-25\\\\198cos\beta=177\ \ \ |:198\\\\cos\beta=\frac{198}{177}\\\\cos\beta\approx0,8939\\\\\beta\approx26,6^o[/tex]
Obliczam γ
[tex]\gamma=180^o-(\alpha+\beta)\\\\\gamma=180^o-(53,8^o+26,6^o)\\\\\gamma=180^o-80,4^o\\\\\gamma=99,6^o[/tex]
