SOLUTION: Two Coast Guard stations, A and B, are on an east-west line and are 120 km apart. The bearing of a ship from station A is N 46o E, and the bearing of the same ship from station
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-> SOLUTION: Two Coast Guard stations, A and B, are on an east-west line and are 120 km apart. The bearing of a ship from station A is N 46o E, and the bearing of the same ship from station
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Question 1120548: Two Coast Guard stations, A and B, are on an east-west line and are 120 km apart. The bearing of a ship from station A is N 46o E, and the bearing of the same ship from station B is N 39o W.
How far is the ship from the east-west line connecting the two Coast Guard stations. Answer by greenestamps(13200) (Show Source):
Draw the figure with station B 120km left (west) of station A, and the ship (point C) south of segment AB. Draw the line CD indicating the (perpendicular) distance of the ship from the east-west line between the two stations.
Let BC=x, so CA = 120-x.
Let d be the length of CD (the distance we are looking for).
Segment CD makes two right triangles BDC and ADC. In those triangles,
tan(39) = x/d
tan(46) = (120-x)/d
Eliminate x between those two equations to find d. It should be easy if you see the right way to do it....
