What is a? There is only one possible value

The cosine rule here can be written as:

12^2 = a^2 + 10^2 - 2*a*10*cos(60deg)

or  a^2 - 20*cos(60deg)*a - 44 = 0

solve the quadratic equation to find a.

Using Law of Sines

sin 60 / 12 = sin b / 10

b = 46.194 degrees

angle A = 180 - 46.194 - 60 = 73.8059 degrees

12 / sin 60 = a / sin 73.8059

a = 13.31 units

Height    AD = sin60 * 10 

CD = cos60 * 10

BD = sqrt(AB² - AD²)

a = CD + BD