Aria ΔABC = (AB*AC*sinA)/2 =[tex] \frac{6*4* \frac{ \sqrt{3} }{2} }{2}=6 \sqrt{3}. [/tex]
In ΔABC => teorema cosinusului =>
[tex]BC^2=AB^2+AC^2-2*AB*AC*cosA[/tex]
[tex]=36+16-2*6*4* \frac{1}{2}=36+16-24=28[/tex]
BC²=28
BC=√28
BC=2√7
P ΔABC = AB+BC+AC=6+4+2√7=10+2√7
[tex]Inaltimea=AD= \frac{2*Aria}{BC}= \frac{2* 6 \sqrt{3} }{2* \sqrt{7} } = \frac{6 \sqrt{3} }{ \sqrt{7} } = \frac{6 \sqrt{21} }{7} [/tex]
