SOLUTION: A ship is sighted from two lighthouses that are 30 km apart on a shore. The angle at the first lighthouse between the shore and the ship is 35 degrees. The angle at the second ligh

Algebra ->  Triangles -> SOLUTION: A ship is sighted from two lighthouses that are 30 km apart on a shore. The angle at the first lighthouse between the shore and the ship is 35 degrees. The angle at the second ligh      Log On


   

Question 961683: A ship is sighted from two lighthouses that are 30 km apart on a shore. The angle at the first lighthouse between the shore and the ship is 35 degrees. The angle at the second lighthouse is 46 degrees. How far is the ship from the second light house?
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Fsin%28A%29=+b%2Fsin%28B%29 we multiply both sides by sin(A) and we get:
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a=+%28b%2Asin%28A%29%29%2F%28sin%28B%29%29
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=
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a=+17.208%2F0.988
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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)