Question

Sa se rezolve triunghiul ABC stiind ca a=2 b=√2 c=1+√3.

Answer 1

Se aplica teorema cosinusuluiSe stiu laturile :a=2;  b=√2 ; c=1+√3. trebuie aflate masura unghiurilor A,B,C.
a²=c²+b²-2bccosA⇒
cos A=(b²+c²-a²)/2bc=[2+(1+√3)²-4]/2×√2×(1+√3)=[2+1+2√3+3-4)/(2√2+2√6)=(2+2√3)/2(√2+√6)=(1+√3)/(√2+√6)
b²=c²+a²-2accosB⇒
cos B=(a²+c²-b²)/2ac=[(1+√3)²+4-2)]/(2×2×(1+√3)=(1+2√3+3+2)/(4+4√3)=(6+2√3)/4(1+√3)=(3+√3)/2(1+√3)
c²=a²+b²-2abcosC⇒
cos C=(a²+b²-c²)/2ab=[4+2-(1+√3)²]/(2×2×√2)=6-1-2√3+3)/4√2=(8-2√3)/4√2=(4-√3)/2√2