Go 641.1 paces at 228 degrees, turn to 166 degrees and walk 157 paces, then trav

Question

Go 641.1 paces at 228 degrees, turn to 166 degrees and walk 157 paces, then travel 196 paces at 160 degrees. What is the direction of the resultant displacement? Use counterclockwise from due East as the positive angular direction, between the limits of -180 and +180 degrees.
I solved for the magnitude of the resultant displacement and got 851.2 paces which was marked as correct. Using that to solve for direction I did the following:
tan-1(Ry/Rx)= tan-1(-372.411/-765.50)= 25.94 degrees
I then subtracted my result from 180 degrees. 180-25.94= 154.06 degrees. The answer was marked incorrect. Any idea how to solve for degrees the correct way?

Explanation / Answer

Here's your mistake: You either add 180 to +25.94 or take away 180 from 25.94. You seemed to have invented the -25.94 degrees. Since you want an answer between -180 and 180, then you take away 180 degrees: 25.94 - 180 = -154.06(+205.94) degrees. That was it though. It's just a small mistake. Here's how you should approach these problems. a negative x-component and a negative y-component indicates that the angle should be in the third quadrant: 154.06 degrees is in the second quadrant which should have told you that you were wrong. On the other hand: -154.06(205.94 degrees) degrees is in the third quadrant.

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