Given right triangle ABCABC with altitude \overline{BD}BD drawn to hypotenuse \overline{AC}AC. If AD=3AD=3 and AC=27,AC=

I'm trying to interpret your question:

 

right triangle(ABC) with right angle(B) and hypotenuse(AC).

 

BD is an altitude.

 

Since AC = 27 and AD = 3, DC = 24

 

Use this relationship:  AD / BD  =  BD / DC

                                      3 / BD  =  BD / 24

                                          BD²  =  72

                                            BD  =  sqrt( 72 )

 

triangle(ADB) with also be a right triangle with hypotenuse AB.

 

use the Pythagorean Theorem:  AD² + BD²  =  AB²:

                 AB²  =  3² + ( sqrt(72) )²

                         ....