Răspuns:
Explicație pas cu pas:
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC} =2R~deci~\frac{2}{sinA} =2*\sqrt{2} ,~sinA=\frac{2}{2*\sqrt{2}},~sinA=\frac{1}{\sqrt{2}},~deci~unghi(A)=\frac{\pi}{4}~sau[/tex]
[tex]unghi(A)=\frac{3\pi}{4}.\\\frac{b}{sinB}=2R,~\frac{\sqrt{6} }{sinB}=2*\sqrt{2},~sinB=\frac{\sqrt{6} }{2*\sqrt{2}}=\frac{\sqrt{3} }{2},~deci \\unghi(B)=\frac{\pi }{3}~sau~\frac{2\pi }{3}.~[/tex]
A doua pereche de unghiuri A,B nu e valabila deoarece unghiurile sunt a triunghiului.
Atunci m(∡A)=45°, iar m(∡B)=60°. ⇒m(∡C)=180°-(45+60)=75°
sin75°=sin(90°-15°)=cos15°
[tex]\frac{c}{sinC} =2R,~sinC=cos15=cos\frac{30}{2} =\sqrt{\frac{1+cos30}{2} }=\sqrt{\frac{2+\sqrt{3} }{4}} =\frac{\sqrt{2+\sqrt{3} } }{2}\\c=2*\sqrt{2}*\frac{\sqrt{2+\sqrt{3} } }{2}=\sqrt{2}*\sqrt{2+\sqrt{3}\\[/tex]
mmmm urât c... :)))
