Question

Aflați măsurile unghiurilor triunghiului ABC știind că m(unghiului A)=6/11 m(unghiului B)=6/19 m(unchiului C).


Vă rog!!!! Rapid!!!!!​

Answer 1

$m(\measuredangle A) = \dfrac{6}{11} \cdot m(\measuredangle B) = \dfrac{6}{19} \cdot m(\measuredangle C) \iff \hat A = \dfrac{\hat B}{\dfrac{11}{6}} = \dfrac{\hat C}{\dfrac{19}{6}}$

știm că:

$m(\measuredangle A) + m(\measuredangle B) + m(\measuredangle C) = 180^{0}$

$\dfrac{\hat A}{\dfrac{6}{6}} = \dfrac{\hat B}{\dfrac{11}{6}} = \dfrac{\hat C}{\dfrac{19}{6}} = \dfrac{\hat A + \hat B + \hat C}{\dfrac{6}{6} + \dfrac{11}{6} + \dfrac{19}{6}} = \dfrac{180^{0}}{\dfrac{6+11+19}{6}} = \dfrac{6 \cdot 180^{0}}{36} = 30^{0}$

atunci:

$m(\measuredangle A) = 30^{0}$

$\dfrac{6}{11} \cdot \hat B = 30^{0} \iff \hat B = \dfrac{11 \cdot 30^{0}}{6} \implies m(\measuredangle B) = 55^{0}$

$\dfrac{6}{19} \cdot \hat C = 30^{0} \iff \hat C = \dfrac{19 \cdot 30^{0}}{6} \implies m(\measuredangle C) = 95^{0}$