Răspuns:
Ex. 59.
[tex]AB=BC=3[/tex]
[tex]AC=3\sqrt{2}[/tex]
[tex]BC^2=AC^2+AB^2-2AB*AC*cosA[/tex]
[tex]=> cosA=\frac{AC^2+AB^2-BC^2}{2AB*AC}=\frac{(3\sqrt{2} )^2+(3)^2-(3)^2}{2*3\sqrt{2}*3 }[/tex]
[tex]=\frac{18}{18\sqrt{2} }=\frac{1}{\sqrt{2} } =\frac{\sqrt{2} }{2}[/tex][tex]=> A=45^*[/tex]
Ex. 60.
[tex]AC=?[/tex]
[tex]BC=\sqrt{2}[/tex]
[tex]m(BAC)=A=30^*[/tex]
[tex]m(ABC)=B=45^*[/tex]
[tex]\frac{a}{sinA}=\frac{b}{sinB} =>b=\frac{a*sinB}{sinA} =\frac{\sqrt{2} *\frac{\sqrt{2} }{2} }{\frac{1}{2} }[/tex]
[tex]=\frac{1}{\frac{1}{2} }=2=> b=2[/tex]
