Find the measure of each angle of triangle abc, given ac=6, cb = 2 square roots of 3, and ab = 4 square roots of 3

Note that

(4sqrt3) ^2 = (2sqrt3) ^2 + 6^2 [ 48 = 12 + 36] so the triangle is a right angled one with hypotenuse AB

So angle C = 90 degrees

sin A = 2 sqrt3 / 4 sqrt3 = 1.2 giving A = 30 degrees

and B = 90 - 30 = 60 degrees

A = 30, B = 60 and C = 90 degrees