A certain sugar is analyzed at an optical laboratory. The tecnician passes two beams in the visible spectra one orange and the other lightblue. These describe the vectors labeled A and B (see the figure from below). Find the modulus of the resultant vector if it is known the radius is 2 micrometers.

The alternatives given on my book are:

$\begin{array}{ll}

1.&2\,\mu m\\

2.&6\,\mu m\\

3.&2\sqrt 3\,\mu m\\

4.&4\, \mu m\\

5.&\sqrt 3\, \mu m\\

\end{array}$

Typically I would try to show some attempt to solve this problem but here I'm stuck at the very beginning. I tried all sorts of manipulations with the vectors. But I couldn't really reach to a logical arrangement to obtain a resultant. In other words I got tangled with too many arrows. Can somebody help me with this?.

If possible I'd appreciate a graphical and simple approach with less algebraic manipulations if possible. Please try to accompany the explanation with some sort of drawing so I can see what's happening because I feel this kind of question does really need that, otherwise I'll not be able to "understand" what's going on.