∴∠ABD=∠CBD (definition of angular bisector)

∵DE⊥AB,DF⊥BC

∴DE=DF (the points with the same distance on both sides of the angle are on the bisector of the angle)

S△ABD = 1/2 ` de ` ab S△BCD = 1/2 ` df ` BC

S△ABC=S△ABD+S△BCD

= 1/2 ` de ` ab+ 1/2 ` df ` BC

= 1/2`DE(AB+BC)

= 1/2 ` de ` 30 = 15 ` de = 36

So DE=36/ 15=2. four

The idea can't be wrong ~O(∩_∩)O~ but I hope it suits you.