Question

un triunghi are masura unghiurilor direct proportionale cu nr 5,10,15. Cea mai mare latura este de 48 cm. Aflati masurile unghhiurilor triunghiului ABC.

Answer 1

[tex]a,b,c=unghiurile\ triunghiului\\ \{a,b,c\}d.p.\{5,10,15\}\Rightarrow \frac{a}{5}=\frac{b}{10}=\frac{c}{15}=k\Rightarrow\\ \Rightarrowa=5k,b=10k,c=15k\\ a+b+c=180\\ 5k+10k+15k=180\\ 30k=180\\ \boxed{k=6}\\ a=5k\Rightarrow a=30\\ b=10k\Rightarrow b=60\\ c=15 k\Rightarrow c=90\\ Asadar\ avem\ un\ triunghi\ dreptunghic\ cu\ ipotenuza\ de\ AB= 48.\\ sin\ b=\frac{AC}{AB}\\ \frac{\sqrt3}{2}=\frac{AC}{48}\Rightarrow AC=24\sqrt3\\ BC^2=AB^2-AC^2\\ BC^2=24^2\cdot4-24^2\cdot3\\ BC^2=24^2\Rightarrow BC=24[/tex]