In an isosceles triangle ABC, the base angle is 60 degrees and the lateral side is 6 cm. Find the base of the triangle.

1. In an isosceles triangle, the angles at the base are equal, therefore, the second angle at the base is 60 degrees.
2. The sum of the angles in a triangle is 180 degrees, therefore, the angle at the apex is equal to the difference between the sum of all angles and the sum of the angles at the base.
3. Apex angle = 180- (60 + 60) = 180-60-60 = 60
4. All angles in a triangle are equal to 60 degrees, from this we conclude that triangle ABC is equilateral.
5. Because the triangle is equilateral, the base is equal to the lateral side.
6. The base is 6 cm.