A lighthouse stands vertically on the shore of a lake. From a point on the opposite shore directly facing the lighthouse, the angle of elevation of its top is \(60
^∘\)
. From another point \(20\ m\) farther away from the lighthouse along the same straight line, the angle of elevation of the top is \(30
^∘\)
. Calculate the height of the lighthouse and the width of the lake. (Use \(\sqrt{3}=1.732\))
Width of the canel \(=\) \(m\)
Height of the canel \(=\) \(m\)
(Note: Enter the answer upto two decimal places.)