A ship is traveling at 18 miles per hour from Corsica to Barcelona, a distance of 350 miles. To avoid harsh weather, the ship leaves Corsica on a route 22°south of the direct route. After 7 hours, the harsh weather has been bypassed. Through what angle should the ship now turn to head directly to Barcelona?

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  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.