Since they form a straight line,
∠AEB + 90° + ∠DEC = 180° → ∠AEB = 90° - ∠DEC
Since there are 180° in a triangle,
∠EDC + 90° + ∠DEC = 180° → ∠EDC = 90° - ∠DEC
Therefore, ∠AEB = ∠EDC and triangle AEB is similar to triangle EDC by AA similarity.
So...
AB = 120/35 * EC And EC = BE
AB = 120/35 * BE
And from the Pythagorean theorem,
AB2 + BE2 = 1202 Substitute 120/35 * BE in for AB .
( 120/35 * BE )2 + BE2 = 1202
576/49 * BE2 + BE2 = 14400
BE2( 576/49 + 1) = 14400
BE = √[ 14400 / (576/49 + 1) ] = 33.6