Question

Sa se calculeze lungimea razei cercului circumscris triunghiului ABC,daca A=π\4, B=π\6, Si AB=6

Answer 1

C=π- A-B
C=π-π/4-π/6
C= 7π/12
sinC= sin(7π/12)= sin(3π/12+4π/12)=sin(π/4+π/3)=  = sin π/4*cos π/3+sin π/3*cos π/4= √2/2 * 1/2 +√3/2 * √2/2= √2/4+ √6/4= 
√2+√6/4 ⇒sin C=√2+√6/4

Aplicam teorema sinusurilor:
AB/sin C=2R 
R=AB/2* sinC
R=6/2*(√6+√2)/4
R=6/√6+√2/2
R=12/√6+√2
Dupa ce rationalizezi vei obtine:
R=3(√6-√2) cm