Answer
The ship is a distance of 14.45 km from point X.
Work Step by Step
Let $a = 15.5~km$
Let $b = 2.4~km$
Let angle $C$ be the angle between these two vectors. Then $C = 180^{\circ}-50^{\circ}- 70^{\circ} = 60^{\circ}$
We can use the law of cosines to find $c$, the distance of the ship from point X:
$c^2 = a^2+b^2-2ab~cos~C$
$c = \sqrt{a^2+b^2-2ab~cos~C}$
$c = \sqrt{(15.5~km)^2+(2.4~km)^2-(2)(15.5~km)(2.4~km)~cos~60^{\circ}}$
$c = \sqrt{208.81~km^2}$
$c = 14.45~km$
The ship is a distance of 14.45 km from point X.
