A right triangle plate ABC with 12 cm long hypotenuse and 60 degree angle B is rotated 90 degrees anticlockwise around point C to the position of triangle a'b'c ', and then along CB

A right triangle plate ABC with 12 cm long hypotenuse and 60 degree angle B is rotated 90 degrees anticlockwise around point C to the position of triangle a'b'c ', and then along CB

∵∠B=60°
∴∠A=180°-60°=30°
∴CB=CB′=12÷2=6,
According to Pythagorean theorem:
AC & sup2; = 12 & sup2; - 6 & sup2; = 108. AC = 6 and root 3
Ψ ab ′ = 6 and radical 3-6 = 6 and radical 3-6
Let X be moved and fall on point G of hypotenuse AB, then Ag = 2x
Then in △ ab'g, (6 radical 3-6) & sup2; + X & sup2; = (2x) & sup2;
The solution is X1 = 2 and radical 3-6 (not in line with the meaning of the question, omit), X2 = 6-2 and radical 3
Moved 6-2 and root 3 cm