Two towers \(AB\) and \(CD\) stand vertically on the same level ground. The angle of elevation of the top \(A\) of the first tower from the foot \(D\) of the second tower is \(60^\circ\), and the angle of elevation of the top \(C\) of the second tower from the foot \(B\) of the first tower is \(30^\circ\). A wire is stretched tightly between the tops \(A\) and \(C\), and its length is \(20\sqrt{21}\) m. The lines of sight \(AD\) and \(BC\) cross each other at a point \(P\).
Identify the following:
(i) The distance between the two towers\(=\) \(m\)
(ii) The heights of both towers
\(AB=\) (\(m\)
\(CD=\) (\(m\)
(iii) The height of the point \(P\) above the ground. \(=\) (\(m\)
Note: Take \(\sqrt{3} = 1.732\) and round off to two decimal places.