
In the triangle ABC we know the length of side BC. Angle ABC = 110o-52o=58o.
Angle ACB = 180o-110o-27o=43o. BD is the
height of the triangle.
Since sin(C)=sin(43o)=BD/187o, then BD=187o*.86=127o.
(1)
Angle A = 180o -58o - 43o = 89o. Angle
ABD = 90o-79o=11o, sin(11o) = .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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