Consider triangle ABC, where angle B is a right angle. Points D and E are chosen on side BC in such a way that the consecutive angles BAD, DAE, and EAC measure 20 degrees, 15 degrees, and 20 degrees, respectively. Given that the length of segment EC is 3 units, your task is to determine the length of segment BD.
Angle B stands firm and strong.
Seeking D and E,
Consecutive angles revealed,
BD's mystery now pursued.