9514 1404 393
Answer:
about 33.4°
Step-by-step explanation:
There are many ways to work this problem. A solution using a geometry program is shown in the attachment. The ship must turn about 33.4° to the north.
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Another way to work this is to redraw the diagram so the initial starting point is left of the origin on the x-axis. Then the ship's direction can be considered to be straight to the right along the x-axis. The origin is the ship's turning point. The ship's destination can be considered to be 350∠22° from the initial position of the ship. The location of that destination relative to the origin represents the turn the ship must make.
At 18 mph for 7 h, the ship has traveled 126 miles.
Using the above method, the ship's destination relative to the origin is ...
(-126, 0) +(350)(cos(22°), sin(22°)) = (198.514, 131.112)
Then the angle the ship must turn is ...
arctan(131.112/198.514) ≈ 33.44°
The ship must turn about 33.4° to the north to head directly to Barcelona.
