In the triangle ABC we know the length of side BC.  Angle ABC  = 110^o-52^o=58^o. 
Angle ACB = 180^o-110^o-27^o=43^o. BD is the height of the triangle.
 
Since  sin(C)=sin(43^o)=BD/187^o, then BD=187^o*.86=127^o.        (1) 

Angle A = 180^o -58^o - 43^o = 89^o.  Angle ABD = 90^o-79^o=11^o,  sin(11^o) = .19.
Therefore AD/AB=.19.                                                                 (2)

By the Pythagorean theorem  AB²=BD²+AD².                              (3)

Substituting (1) & (2) into (3), we find that AB²=127²+(.19*AB)².
Therefore the distance to the island from point B is 128 meters.

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