By applying cosine rule for the given triangle, we get cosC=
b2+a2−c2
2ab
Therefore, we substitute the given values of both the sides and the included angle C to obtain the value of the third side. cosC=cos(
π
3
)=
1
2
∴
1
2
=
b2+a2+c2
2ab
ab=b2+a2−c2 (1+√3)(2)=(1+√3)2+4−c2 2+2√3=4+2√3+4−c2 c2=8−2=6 c=√6 Now applying sine rule to the above set of sides and thee given angle C, we get
a
sinA
=
b
sinB
=
c
sinC
c
sinc
=
√6
sin(60°)
=
2√6
√3
=2√2
b
sinB
=2√2 sinB=
b
2√2
=
2
2√2
=
1
√2
B=45° Now, two of the angles are known. Hence we can find the third angle using angle sum property of a triangle. Therefore we get angle B as A=180°−(45°+60°) =75°