As shown in the figure, the right angle triangle plate ABC with the inclined edge length of 6cm and ∠ a = 30 ° rotates 90 ° clockwise around point C to the position of △ a ′ B ′ C, and then translates to the left along CB so that point B ′ falls on the inclined edge ab of the original triangle plate ABC. Then the distance of the triangle plate's left translation is___ cm．

Let the triangle plate intersect with ab at point d after translation to the left; so the distance of translation to the left of the triangle plate is the length of b'd. ∵ AB = 6cm, ∵ a = 30 °∵ BC = b'c = 3cm, AC = 33cm ∵ b'd ∥ BC, ∵ b'dbc = ab'ac, that is, b'd3 = 33-333 ∥ b'd = (3-3) cm; so the distance of translation to the left of the triangle plate is (3-3) cm

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