Răspuns:
Explicație pas cu pas:
Cf T Pitagora generaliazata:
BC²=AB²+AC²-2AB×AC×cosA
cosA=cos60°=1/2
BC²=16+36-2×4×6×1/2= 52-24=28 BC=2√7
R=abc/4S
p=(4+6+2√7)/2=5+√7
S=√(5+√7)(1+√7)(√7-1)(5-√7)=√(25-7)(7-1)=√18×6=6√3 cm²
R=4×6×2√7/6√3=8√7/√3=8√21/3
AB = 4, AC = 6, A=π/3
cos π/3=1/2
sin π/3=√3/2
Teorema cosinusului:
BC²=AB²+AC²−2•AB•AC•cosA
BC²=16+36-2•4•6•1/2=52-24=28
BC=2√7
Teorema sinusurilor:
AB/sinC=AC/sinB=BC/sinA=2R
din BC/sinA=2R => R=BC/2sinA
R=2√7/(2√3/2)
R=2√7/√3
sau: R=2√21/3
