Final answer:
To determine the total distance traveled by the ship, one would need to know the lengths of each leg of the journey and use the law of cosines or vector addition to solve. However, only the distance of the first leg from point C to point A is provided at 100 miles.
Step-by-step explanation:
The question asks us to determine the total distance a ship travels given a series of directional movements. The ship starts from point C, moves due north to point A, then travels at a 60° angle east of north to point B, and finally returns to point C at a 45° angle west of south.
From point C to A, the ship travels a straightforward 100 miles due north. Now, at point A, the direction changes 60° east of north, and at point B, it returns to point C at an angle of 45° west of south.
While the exact mileage for the second and third legs isn't given, the total distance traveled by the ship would be the sum of the lengths of all three legs of the trip. To solve for this we would most likely need to use the law of cosines or vectors if those distances were known. As it stands, only the first 100 miles are certain.
The described problem is similar to vector addition and subtraction problems that involve graphical representations to calculate total distance or displacement.