As shown in the figure, the hypotenuse ab of the right angle triangle plate ABC is 12cm, ∠ a = 30 °, rotate the triangle plate ABC clockwise 90 ° around C to the position of triangle plate a'b'c ', and then translate it to the left along the CB direction, so that the point B' falls on the hypotenuse ab of the original triangle plate ABC, then the translation distance of triangle plate a'b'c 'is () A. 6cmB. 4cmC. （6-23）cmD. （43−6）cm

As shown in the figure, the hypotenuse ab of the right angle triangle plate ABC is 12cm, ∠ a = 30 °, rotate the triangle plate ABC clockwise 90 ° around C to the position of triangle plate a'b'c ', and then translate it to the left along the CB direction, so that the point B' falls on the hypotenuse ab of the original triangle plate ABC, then the translation distance of triangle plate a'b'c 'is () A. 6cmB. 4cmC. （6-23）cmD. （43−6）cm

As shown in the figure, B ′ D ⊥ AC is made through B ′ and the perpendicular foot is B ′, ∵ in RT △ ABC, ab = 12, ∵ a = 30 °, ∵ BC = 12ab = 6, AC = ab · cos30 ° = 63. According to the nature of rotation, B ′ C = BC = 6, ∵ ab ′ = AC-B ′ C = 63-6. In RT △ ab ′ D, ∵ a = 30 °, ∵ B ′ d = ab ′· tan30 ° = (63-6) × 33 = (6-23) cm