Question

aflati masurile unghiurilor unui triunghi ABC stiind ca acestea sunt invers proportionale cu nr 2 ,3,6 . Clasificati triunghiul dupa unghiuri si laturi ... cat de urgent se poate !!! va rog !!

Answer 1

$\it Fie\ x,\ y, \ z \ masurile\ celor\ trei\ unghiuri.$

$\it \{x, y, z\} \ invers\ proportionale \ cu\ \{2,\ 3,\ 6 \} \ \Longrightarrow$

[tex]\Longrightarrow \it 2x =3y=6z =k \Longrightarrow \begin{cases} x=\dfrac{k}{2} \\ \\ y=\dfrac{k}{3} \\ \\ z = \dfrac{k}{6}\end{cases}[/tex]

[tex]\it x+y+z = 180^0 \Rightarrow \dfrac{k}{2}+\dfrac{k}{3}+\dfrac{k}{6} \Rightarrow k(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}) =180^0 \Rightarrow \\ \\ \Rightarrow \ k \cdot1 = \it180^0 \Rightarrow k = 180^0[/tex]

[tex]\it x= \dfrac{180^0}{2} =90^0 \\ \\ \ \it y= \dfrac{\it 180^0}{3} = \it60^0 \\ \\ \ \it z= \dfrac{\it 180^0}{6} = \it30^0 [/tex]