edit: If I'm understanding correctly you've done using your carried forward error in .
If you do
AZ = AY = 2 - we are told this. We also know angle A is 60 degrees as it's a property of equilateral triangles.
. In this example c = YZ - the side we want to know, a = AZ = 2, b = AY = 2 and C = A = 60 degrees (angle A)
Thus YZ is 2 units across. It has been established that BC = 3 and so the ratio of YZ to BC is 2:3
Similarly the ratio of BC to YZ is the reciprocal which is 3:2