Basic Physics Question, Confused, Please Help!

Calculate algebraically the resultant of the following co-planar displacements; 20m at 30 degrees, 40m at 120 degrees, 25m at 180 degrees, 42m at 270 degrees, 12m at 315 degrees.
I know that the answer is 20.1 at 197 degrees but I really don't know how to get there, can someone please help me through the process.

You could just do vector addition:
1st the horizontal components
20cos30 + 40cos120 + 25cos180+42cos270 + 12cos315 = -19.2
Next the vertical components
20sin30 + 40sin120 + 25sin180+42sin270 + 12sin315 = -5.8

Magnitude = sqrt[19.2*19.2+5.8*5.8] = 20.07
Angle is arctan [-5.8/-19.2] = 16.8 + 180 = 196.8 deg ( you know it is going to be in the third quadrant:180 deg to 270 deg because that is the only place where x and y are negative)

If you are trying to get to the answer 20.1m at 197 degrees , You multiply from meters to the degree , algebraically , you have to displace them at the degree , but in terms , the speed if co - planar displacements , at the plane makes it at the process of multiplying of how it is displaced , like 20m at 30 degrees , reaches 40m at 120 degrees , it is displaced pretty much more in the process , 25m at 180 degrees , The orgin is from 20m , where you began the process . So very close angular displacements , to the degrees if displacements .

Get the x and y components of each.

X1 = 20 cos 30 = 17.32
Y1 = 20 sin 30 = 10
X2 = 40 cos 120 = –20
Y2 = 40 sin 120 = 34.64
X3 = 25 cos 180 = –25
Y3 = 25 sin 180 = 0
X4 = 12 cos 315 = 8.49
Y4 = 12 sin 315 = –8.49

draw a vector diagram to be sure you have the polarities right

Rx = 17.32 – 20 – 25 + 8.49 = –19.19
Ry = 10 + 34.64 – 8.49 = 36.15

R = √(19.19² + 36.15²) = 40.93
θ = arctan (Ry/Rx) = θ = arctan (–36.15/19.19) = –63.3º

I don't match your numbers, but the method is correct. Check my math,