Answer:
The northern lighthouse is approximately  closer to the boat than the southern lighthouse.
 closer to the boat than the southern lighthouse.
Step-by-step explanation:
Refer to the diagram attached. Denote the northern lighthouse as  , the southern lighthouse as
, the southern lighthouse as  , and the boat as
, and the boat as  . These three points would form a triangle.
. These three points would form a triangle.
It is given that two of the angles of this triangle measure  (northern lighthouse,
 (northern lighthouse,  ) and
) and  (southern lighthouse
 (southern lighthouse  ), respectively. The three angles of any triangle add up to
), respectively. The three angles of any triangle add up to  . Therefore, the third angle of this triangle would measure
. Therefore, the third angle of this triangle would measure  (boat
 (boat  .)
.) 
It is also given that the length between the two lighthouses (length of  ) is
) is  .
. 
By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question,  is opposite to side
 is opposite to side  , whereas
, whereas  is opposite to side
 is opposite to side  . Therefore:
. Therefore:
 .
.
Substitute in the known measurements:
 .
.
Rearrange and solve for the length of  :
:
 .
.
(Round to at least one more decimal places than the values in the choices.)
Likewise, with  is opposite to side
 is opposite to side  , the following would also hold:
, the following would also hold:
 .
.
 .
.
 .
.
In other words, the distance between the northern lighthouse and the boat is approximately  , whereas the distance between the southern lighthouse and the boat is approximately
, whereas the distance between the southern lighthouse and the boat is approximately  . Hence the conclusion.
. Hence the conclusion.