Answer
The ship is a distance of 39.2 km from point A.
Work Step by Step
Let $a = 18.5~km$
Let $b = 47.8~km$
Let angle $C$ be the angle between these two vectors. Then $C = 180^{\circ}-47^{\circ}- 81^{\circ} = 52^{\circ}$
We can use the law of cosines to find $c$, the distance of the ship from point A:
$c^2 = a^2+b^2-2ab~cos~C$
$c = \sqrt{a^2+b^2-2ab~cos~C}$
$c = \sqrt{(18.5~km)^2+(47.8~km)^2-(2)(18.5~km)(47.8~km)~cos~52^{\circ}}$
$c = \sqrt{1538.23~km^2}$
$c = 39.2~km$
The ship is a distance of 39.2 km from point A.
