Question 961683
You can find the sides of a triangle if you know:
AAA (three angles)
AAS (two angles and a side NOT in between the angles)
ASA (two angles and a side between)
etc.
In your problem we know two angles, 35 and 46, and the side in between them (30 km)so we will use ASA. 
First we find the missing angle. The angles in every triangle, no exceptions, add up to 180. So, 180-(35+46)= 99 is our 3rd angle
ASA says that, to find side a (the side opposite to angle A):
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{{{a/sin(A)= b/sin(B)}}} we multiply both sides by sin(A) and we get:
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{{{a= (b*sin(A))/(sin(B))}}} 
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= {{{a= 30(sin(35))/(sin(99))Now let's plug in the numbers, get your calculator out and find sin(35) and sin(46):
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{{{a= (30(0.5736))/0.988}}}
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{{{a= 17.208/0.988}}}
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{{{a= 17.42}}} This is the distance from the second light house to the ship.
See the sketch I made for you (always draw these problems so you can visualize them)  *[illustration ASA.jpg]