Then, ∠ b = 30.

Therefore, ∠ BAC =180-30-30 =120

If BA⊥DA is known, then ∠ bad = 90.

Therefore, ∠ DAC = 120-90 = 30

So, AD=CD.

Let ad = cd = x.

In Rt△ABD, ∠ b = 30.

Then BD=2AD=2x.

Therefore, BC=BD+CD=2x+x=3x.

BC=6 is known.

So 3x=6.

Then x=2.

Therefore, AD=2 and BD=4.

So, from Pythagorean theorem, we get: AB? =BD？ -Advertising? = 16-4= 12

Therefore, AB=√ 12=2√3.