This one's tricky since it doesn't expressly state that it's a 30/60/90 triangle, so it'll take a little more work... Something to note however, is that if the side lengths fulfill the 30/60/90 triangle requirements, then we can assume it is a 30/60/90 triangle. Start with the Pythagorean theorem to find x:
[(6root3)^2+(6)^2=x^2]. With this, we find that x = 12. So now we also know it is a 30/60/90 triangle since the longer leg (12) is twice the size of the shorter leg (6) and the hypotenuse (6root3) is the shorter leg multiplied by root 3. From here it's safe to assume that you're going to have to find how x is split by the line 'y'. To do this, we can see that the line splits the whole triangle into two other 30/60/90 triangles. Using the one to the right, we find the shorter leg is 2root3 (6/root3 -> 6root3/3 -> 2root3), and then we can show that y = 4root3 due to the principles of a 30/60/90 triangle.
I'd love to show this all on paper, I know it's VERY confusing in words, but I'm not sure if I'd be able to add pictures on here. Lemme know if this needs more explaining.
