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that was unnecessary  

Pythagorean theorem:
                       AB = √30^2 + 16^2 = 34

These are similar triangles.

∠BAC is congruent to ∠BAD
∠ACB is congruent with ∠ABD (both right angles)

Using ratios:
               AC / AB = AB / (AC + CD)
             AC + CD =  AB² / AC
                       CD = AB² / AC - AC
                       CD = 34² / 16 - 16               
                       CD = 56.25
The answer to this question is 56.