In a right-angled triangle ABC with angle A = 90 °, angle C = 60 °, BC = 20cm. Find AC.

By condition, we are given a right-angled triangle, in which one of the angles is 90 degrees, the second is 60 degrees, which means that by the property of the triangle (the sum of all the angles of the triangle is 180 degrees), the angle B is 30 degrees.
By condition, the hypotenuse is 20 cm.
We know that in a right-angled triangle, a leg lying opposite an angle of 30 degrees is equal to half the hypotenuse. The leg that lies opposite an angle of 30 degrees is AC, the one that we need to find.
Accordingly: AC = 20: 2 = 10 (cm).
Answer: 10 cm.