A ship leaves port on a course with a bearing of 20 degrees. After sailing in that direction for 76 kilometers, it changes course to a bearing of 105 degrees and travels for 143 km. If the ship went directly back to Port, what bearing did it take?

I'm not quite getting the right answer :(

1 Answer
Mar 4, 2018

Don't confuse "bearing" (compass point) with "angle" direction from origin.


The triangle has a side of 76 pointed "up" - 20 degrees right of the y-axis (bearing) rather than off of the x-axis (angle). The turn to a bearing of 105 is a slope downward (greater than 90 from the y-axis, or under the x-axis). That makes a side of 143.
The question is what "bearing" must be taken to reach the origin again. From the dimensions, the outward-bound angle after the turn is 95.
Drawing out the diagram should help.
Proceed from there trigonometrically. A quick geometric construction shows a return bearing of 285 (360 - 75). Distance approximately 168.