The vertex angle measures 120 deg.
The base angles are congruent.
Each of the base angles measures x, so
x + x + 120 = 180
2x = 60
x = 30
The altitude separates the isosceles triangle into two 30-60-90 right triangles.
The ratio of the lengths of the sides of a 30-60-90 triangle is
short leg : long leg : hypotenuse
1 : sqrt(3) : 2
The hypotenuse is twice the length of the short leg.
Look at one of the right triangles.
The hypotenuse is the leg of the isosceles triangle.
It has a length of 8 units.
The altitude of the isosceles triangle is the short leg of the right triangle.
The short leg is half the hypotenuse, so the altitude of the isosceles triangle is 4 units.
The length of the base of the isosceles triangle is twice the long leg of each right triangle. The long leg of the right triangle measures sqrt(3) times the length of the short leg. Each long leg has length 4sqrt(3). The base is twice that, so the base has length 8sqrt(3) units.
