Question 1014765
You have to draw this to have any chance to solve it.
The angle from the boat to the top of the lighthouse is 14d52m by alternate interior angles.  The tangent of that is 200/x, where x is the first distance.
x tangent 14d52m equals 200
200/tangent 14d52 m =x
x=753.4189'
In the same fashion
200/tangent 45d10' is the final distance.  That is 198.84 feet away. 
If you do this all without rounding, it will be 554.58 feet (753.42-198.84) the boat moved.