Question

Scrieti unghiurile triunghiurile ABC in ordinea crescatoare a masurilor lor, daca: AB/AC >1,2 BC/AC < 0,8.

Answer 1

[tex]\it \dfrac{AB}{AC} \ \textgreater \ 1,2\ \textgreater \ 1 \Rightarrow AB\ \textgreater \ AC \Rightarrow AC\ \textless \ AB \Rightarrow m(\hat B) \ \textless \ m(\hat C) \ \ \ \ (1) \\\;\\ \\\;\\ \dfrac{BC}{AC} \ \textless \ 0,8 \ \textless \ 1 \Rightarrow BC\ \textless \ AC\Rightarrow m(\hat A) \ \textless \ m(\hat B) \ \ \ \ (2) \\\;\\ \\\;\\ (1), (2) \Rightarrow m(\hat A) \ \textless \ m(\hat B) \ \textless \ m(\hat C) . [/tex]  

Answer 2

AB>AC (1)
BC<AC deci AC>BC (2)
 
atunci din (1) si (2) ⇒AB>AC>BC
 cum la latura cea mai mare corespunde unghiul cel mai mare
 ∡C > ∡B >∡A
as simple as that!