geometry
posted by tasha .
BC is an altitude with length of 30 of ƒ´ABD. AC has a length of 16 What is the length of CD? If necessary, round your answer to two decimal places.

I do not understand the meaning of the ƒ´ symbol that appears in front of ABD. Is ABD a triangle?
If BC is an altitude of the triangle ABD, then the Pythagorean theorem tells you that AC = sqrt[(16)^2 +(30(^2] = 34. The angle at A is therefore
arctan (15/8) = 61.93 degrees
You don't have enough information to say what BD, AD and CD are unless ABD is also a RIGHT triangle. If it is, BD = 34*tan61.93 = 63.75;
AD = 34/cos61.9 = 72.26
CD = AD  AC = 38.26