A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point $A$, with uniform speed. At that point, angle of depression of the boat with the man's eye is $30 ^ { \circ }$ (Ignore man's height). After sailing for 20 seconds, towards the base of the tower (which is at the level of water), the boat has reached a point $B$, where the angle of depression is $45 ^ { \circ }$. Then the time taken (in seconds) by the boat from $B$ to reach the base of the tower is : (1) 10 (2) $10 ( \sqrt { 3 } - 1 )$ (3) $10 \sqrt { 3 }$ (4) $10 ( \sqrt { 3 } + 1 )$
A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point $A$, with uniform speed. At that point, angle of depression of the boat with the man's eye is $30 ^ { \circ }$ (Ignore man's height). After sailing for 20 seconds, towards the base of the tower (which is at the level of water), the boat has reached a point $B$, where the angle of depression is $45 ^ { \circ }$. Then the time taken (in seconds) by the boat from $B$ to reach the base of the tower is :\\
(1) 10\\
(2) $10 ( \sqrt { 3 } - 1 )$\\
(3) $10 \sqrt { 3 }$\\
(4) $10 ( \sqrt { 3 } + 1 )$