The topmost point of a perfectly vertical pole is marked A. The pole stands on a flat ground at point D. The points B and C are somewhere between A and D on the pole. From a point E, located on the ground at a certain distance from D, the points A, B and C are at angles of 60, 45 and 30 degrees respectively. What is AB : BC : CD?

A

$$(3 + \sqrt 3) : (1 + \sqrt 3) : 1$$

B

$$(3 - \sqrt 3) : 1 : (\sqrt 3 - 1)$$

C

1 : 1 : 1

D

$$(3 - \sqrt 3) : (\sqrt 3 - 1) : 1$$

E

$$(\sqrt 3 - 1) : 1 : (3 - \sqrt 3)$$