Concerning labs . . .
Let us agree that the vector projections which coincide w/
     the negative X-axis (left of origin) are negative.
Thus, we enter their values in the table w/ a negative sign:

 vctr    radius    theta      \    x-prjctn      y-prjctn
   1           200    30         \       173           100           x=r*cos(theta)
   2           150    45         \       106           106           y=r*sin(theta)
   3           175    120       \        -87.5        152
                                                                              R=sqr(x^2+
       - - - - -                           sum-x       sum-y                +y^2)^1/2
                                               192           358
                                                                              theta =
                 R =   406    \    r-theta =  62 deg                   invtan(y/x)
                                       eq-theta =  242 deg
        - - - - -
Now, 'you' should sketch to scale for your further edification.
     (What else would you be doing while snow-bound?)

Sketch (rough)