Question

cau 14,15 nha cac b

Answer 1

14:

Xét ΔABC có \(cosA=\dfrac{AB^2+AC^2-BC^2}{2\cdot AB\cdot AC}\)

=>\(4+9-BC^2=2\cdot2\cdot3\cdot\dfrac{-1}{2}=-6\)

=>BC^2=13+6=19

=>BC=căn 19(cm)

\(S_{ABC}=\dfrac{1}{2}\cdot AB\cdot AC\cdot sinBAC=\dfrac{1}{2}\cdot2\cdot3\cdot\dfrac{1}{2}=\dfrac{3}{2}\)

Xét ΔABC có \(\dfrac{BC}{sinA}=2R\)

=>2R=căn 19:1/2=2*căn 19

=>R=căn 19

Xét ΔABC có AD là phân giác của góc BAC

nên \(AD=\dfrac{2\cdot AB\cdot AC}{AB+AC}\cdot cos60=\dfrac{2\cdot2\cdot3}{2+3}\cdot\dfrac{1}{2}=\dfrac{6}{5}\)