Trigno problem. Expressing values in terms of and showing...

Me again. (Hi)

Okay, for this question that I'm having difficulty in, here is the figure:

http://usera.ImageCave.com/biosyn/qam.PNG

And as we know:

sin30= under.root (1/4)

cos30= under.root (3/4)

This question is divided into 2 parts.

i) express each of AC and BC exactly in terms of L, and show that

AB=(1/2)L under.root7. (Note: how do I write mathematical symbols in this forum?)

I used pythagoras method and sin30=perpendicualr/hypotenuse to get values of DC and AC, but the problem is, they are coming as fraction under.root values rather then whole numbers. This wouldn't be a problem if there weren't any conditions to have under.root solutions. E.g, I'm getting AC as L under.root 3/4. I then have to apply THIS to get DC and subsequently, BC (twice DC), from pythag method. DC comes as (1/2)L therefore BC becomes L. Is this correct?

ii) Even though I was able to prove AB as (1/2)L under.root7, when applying in this part of the question, it doesn't work. Here is says: Show that x=tan^-1(2/under.root3) -30.

I'm doing this like this: tan (x+30) = BC/AC

tan (x+30) = L/L under.root (3/4).

x = tan^-1 [L/L under.root (3/4)] -30

this is wrong but I do not know how to solve this. How do I do this?