a=13 b=18 c=26

http://en.wikipedia.org/wiki/Law_of_cosines

a=13 b=18 c=26
cos Alpha = (b² + c² - a²) / (2*b*c)
cos Beta = (c² + a² - b²)/(2*c*a)
Gamma=180-Alpha-Beta

a=13; b=18; c=26; acos((b^2 + c^2 - a^2) / (2*b*c)) = 27.399361586368°

a=13; b=18; c=26; acos((c^2 + a^2 - b^2)/(2*c*a)) = 39.582305569896°

180 - 27.399361586368 - 39.582305569896= 113.018332843736°

verification with http://en.wikipedia.org/wiki/Law_of_sines

$${\frac{{\mathtt{13}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{27.399\: \!361\: \!586\: \!368}}^\circ\right)}}} = {\mathtt{28.249\: \!208\: \!025\: \!435\: \!121\: \!1}}$$ $${\frac{{\mathtt{18}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{39.582\: \!305\: \!569\: \!896}}^\circ\right)}}} = {\mathtt{28.249\: \!208\: \!025\: \!418\: \!069\: \!5}}$$ $${\frac{{\mathtt{26}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{113.018\: \!332\: \!843\: \!736}}^\circ\right)}}} = {\mathtt{28.249\: \!208\: \!025\: \!404\: \!428\: \!1}}$$