Question

cac giai giai dum` minh cau 12,13 nha cam on may b

Answer 1

13:

\(S_{ABC}=\dfrac{1}{2}\cdot AB\cdot AC\cdot sinBAC=\dfrac{1}{2}\cdot5\cdot8\cdot\dfrac{\sqrt{3}}{2}=\dfrac{4\sqrt{3}}{2}\cdot5=10\sqrt{3}\)

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

=>\(5^2+8^2-BC^2=2\cdot5\cdot8\cdot cos60=40\)

=>BC^2=49

=>BC=7

S=pr

=>r*(5+8+7)/2=10căn 3

=>r=10căn 3/10=căn 3

Xét ΔABC có

BC/sinA=2R

=>2R=7:sin60=7*2/căn 3

=>R=7/căn 3