Answer:
109°
Explanation:
You want to know the bearing of a ship from its starting location after it sails 10 miles on a bearing of 74°, then 15 miles on a bearing of 131°.
Final bearing
We can add the travel vectors and express the result in polar form. The angle of that is the bearing angle from the starting position. The calculator result is shown in the second attachment.
The ship is at a bearing of 109° from its starting position.
Vector sum
The first attachment shows a diagram of the vector sum. The triangle internal angle opposite the resultant vector is shown. The two triangle side lengths (10 mi, 15 mi) can be used with the law of cosines to find the distance (OB) the ship is from its starting location.
Knowing that distance, we can use the law of sines to find angle AOB. Adding that angle to the initial bearing gives the bearing to the final location. The calculations for this are shown in the third attachment.
The ship is at a bearing of 109° from its starting position.
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Additional comment
Of course, the geometry app used to draw the diagram in the first attachment can also measure the bearing to the final location.
The upshot is there are several ways to find the bearing of the final position.
The rectangular coordinates we use with the calculator for vector calculations are (north, east) coordinates. This avoids having to switch to angles measured counterclockwise from +x, and then back again to angles measured clockwise from +y.
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