These angles are special angles.
Use your rules for a 45-45-90 triangle and then use your
rules for a 30-60-90 triangle.
Rationalizing the denominator, we get
This value is the hypotenuse of the 30-60-90 triangle,
so we have CB as the short leg and it's equal to one-half the hypotenuse...
And...AB is the long leg which is the short leg times the square root of 3.