Two boats set sail in the evening, with the intention of making dock the next mo

Question

Two boats set sail in the evening, with the intention of making dock the next morning. Boat A travels east for 1240m, then turns north and travels 1600m, making port at the dock. Boat B sails north for 1960m, and a storm knocks out the navigation. Calculate the vector that will take Boat B to the dock, specify both direction and magnitude.

I did 1960-1600, so boat B must sail 360m south. And 1240m east.

So the magnitude is.....

Ax = 1240m, Ay = -360m

Sqrt (Ax^2+Ay^2) = 1291.2m

Then arctan (1240/360) = 73.81 degrees

So boat B must travel 1291.2m at 73.81 degrees SE to reach port. Is this correct?

Explanation / Answer

it depends how you set up your coordinate system. I don't teach your class so I can't be sure, but arctan(y/x)=angle is the way to set it up. Otherwise it looks good. (you used x/y)

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