[[[[ 1]]]]

This can be obtained from cosine theorem.

- 1/2=cos 120？ =cosB=(a？ +c？ -B? )/(2ac)=(a？ +2-6)/(2a√2)

Namely: a? +(√2)a-4=0

(a-√2)(a+2√2)=0

∴a=√2.(a=-2√2 is omitted)

∴a=√2

[[[2]]]

A=60？ ，b= 1，S=(√3)/2

Formula by area

(√3)/2 = S =( 1/2)(BC)sinA =(c/2)sin 60？ =(c/4)×√3。

∴c=2.

This can be obtained from cosine theorem.

1/2=cos60？ =cosA=(b？ +c？ -a？ )/(2bc)=(5-a？ )/4

Namely (5-a? )/4= 1/2

Answer? =3

a=√3

[[[3]]]

From the title and sine theorem, we can get

a/sinA=c/sinC=2c/(√3)

∴sinC=(√3)/2

Combining C as an acute angle, we can get C=60?