ACF is a 30º-60º-90º triangle because of the following:
1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 :

1 → short leg
2 → hypotenuse
→ long leg
Side length of the hexagon is the short leg of the triangle. It is 1.
r1 is the radius of the incircle in a regular hexagon. 2(r1) is the diameter of the incircle. It is also the hypotenuse of the right triangle. It is 2.
Using Pythagorean theorem.






