Two forces, one of 120 pounds and the other of 200 pounds, act on the same object at angles of 30° and -30° respectively, with the positive x-axis. Find
the direction of the resultant of these two forces.

9514 1404 393

  -8.21°

Step-by-step explanation:

The horizontal and vertical components of the forces are ...

  (120; 30°) = (103.923, 60}

  (200; -30°) = (173.205, -100}

Then the resultant is ...

  (103.923 +173.205, 60-100) = (277.128, -40)

and the resultant direction is

  arctan(-40/277.128) = -8.21°

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The polar coordinates (A; β) can be translated to rectangular coordinates by ...

  (A; β) = (A·cos(β), A·sin(β))

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Additional comment

The semicolon in (A; β) signifies the ordered pair is polar coordinates (magnitude; angle). The comma in (x, y) signifies the ordered pair is rectangular (Cartesian) coordinates. This notation is borrowed from the GeoGebra app, a geometry graphing/calculating program. It avoids some confusion. Personally, I prefer the notation A∠β to signify a magnitude and direction in polar coordinates.