As shown in the figure, in RT △ ABC, ∠ ACB = 90 ° AB = 6, P is the point on AB, connect PC, set ∠ BCP = m ∠ ACP, when AP = 3 / 2, whether there is a positive integer m, Make PC perpendicular to ab? If it exists, calculate the value of M. if it does not exist, explain the reason
If there is a positive integer m, let BC = x, AC = √ 36-x ^ 2, ab = 6, AP = 3 / 2, then BP = 9 / 2 in right triangle BCP, sin ∠ BCP = BP / BC = 9 / 2x in right triangle ACP, sin ∠ ACP = AP / AC = 3 / 2 √ 36-x ^ 2, and ∠ BCP + ∠ ACP = ∠ ACB = 90 ° in right triangle ACP