Answer:
241°
Step-by-step explanation:
You are given the triangle internal angle (N) at Naples = 46°, and the side opposite a = 765 km. You are given the side b = 515 km, and asked to find an angle related to the internal angle opposite (C).
By the law of sines, the internal angle (C) at Canton is ...
sin(C)/b = sin(N)/a
C = arcsin((b/a)sin(N)) = arcsin(515/765·sin(46°)) ≈ 28.964°
The bearing from Elgin to Canton will be 270° less this angle, so is about 241°.
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Comment on your answer
Apparently, you added 29° to 270°, rather than subtracting. Since the direction from Elgin to Canton is south of west, the bearing angle must be between 180° and 270°. Note that a line west from Elgin will be parallel to the line east from Canton, so you can take advantage of alternate interior angles being congruent where the Elgin-Canton line crosses those parallel east-west lines.
