Looking at the big right triangle ABC, and the
fact that the tangent is 



Use the inverse tangent on a calculator to find ∠A:

∠A = 53.13010235°

We know that ∠ABD is 45° because BD bisects the right angle at B

We find ∠ADB by using the fact that
the sum of the interior angles of ᅀABD is 180°

∠A + ∠ABD + ∠ADB = 180° 

∠ADB = 180° - ∠A - ∠ABD

∠ADB = 180° - 53.13010235° - 45° = 81.86989765°

So we use the law of sines:



Cross-multiplying:



Divide both sides by :
  




Work out the right side with a calculator:

AD = 2.142857143cm

Edwin