NDA Math Properties of Triangles

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°