Question

If AD=6 and AB=24, find AC

Answer 1

When a perpendicular is dropped from the right-angle (C) to the opposite side AB, the metric relations apply:
BD*BA=a^2 ..........................(1)
AD*AB=b^2...........................(2)
BD*DA=DC^2........................(3)

Given AD=6, AB=24, using metric relation (2) above, we have
b^2=6*24=144
=>
b=sqrt(144)=12

By the way, we conclude that this is a 30-60-90 triangle because b/AB=(1/2)=sin(B) => B=30 degrees.

Answer: b=12