Question 614175: How would you do this??
Two coast guard stations located 65 miles apart on a north to south line each receive a radio signal from a ship at sea. From the northernmost station, the ships bearing is 114 degrees. From the other station, the ships bearing is 44.8 degrees. How far is the ship from the northernmost station?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Two coast guard stations located 65 miles apart on a north to south line each receive a radio signal from a ship at sea. From the northernmost station, the ships bearing is 114 degrees. From the other station, the ships bearing is 44.8 degrees. How far is the ship from the northernmost station?
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Bearing are measured clock-wise from North.
The interior angle A of the bearing 114 degs = 66 degs.
The interior angle B of the bearing 44.8 = 44.8 degs
The 3rd angle, C = 69.2 degs
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A is the northern point
B is the southern point
The 65 mile side between station is side c.
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Side b is the distance from the northern point to the the ship
Use the Law of Sines:
c/sin(C) = b/sin(B)
b = c*sin(B)/sin(C)
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