Question 1121379
the problem states it is giving bearings but really they are directions.
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The direction to a point is stated as the number of degrees east or west of north or south.
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The bearing to a point is the angle measured in a clockwise direction from the north line.
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I am using the information given as directions not bearings
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we need the internal angles of the triangle that joins the ship with stations A and B
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90 degrees - 54 degrees = 36 degrees and 90 degrees - 31 = 59 degrees and the third angle at the ship is 180 - 36 -59 = 85 degrees
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now use the law of sines
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a) sin(36) = distance from ship to AB / 61.9518  
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distance from ship to AB = sin(36) * 61.9518 = 36.4144 km
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b) 72/sin(85) = distance from A to ship / sin(59)
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distance from A to ship = 72 * sin(59) / sin(85) = 61.9518 km
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c) 72/sin(85) = distance from B to ship / sin(36)
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distance from B to ship = 72 * sin(36) / sin(85) = 42.4822 km
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