Vectors approximate sum

[rasilva]

What is the approximate sum of the following two vectors? Magnitude 20 at 30° and magnitude 10 at 60°.

Please explain

[Kalbi_Rob]

What is the approximate sum of the following two vectors? Magnitude 20 at 30° and magnitude 10 at 60°.

Please explain
First you have to convert to rectangular (Cartesian)

x=r*cosθ and y=r*sinθ

x1=20 cos(30) = 17.32
y1= 20 sin(30) = 10
x2=10 cos(60) = 5
y2= 10 sin(60) = 8.66

Now add them together:

x3= x1+x2 = 22.32
y3= y1+y2= 18.66

Now convert back to polar:

r=sqrt((x^2)+(y^2)) tanθ=(y/x)

r=sqrt((22.32)^2+(18.66)^2) = 29.09

θ=tan^(-1) (18.66/22.32) = 39.9

Thus we end up with an answer of:
29.09<39.9o

So, in general, you can add/subtract rectangular forms.
You can also multiply/divide polar magnitudes(angles are added when multiplying and subtracted when dividing).

Great references for this math below:

https://www.mathsisfun.com/polar-cartesian-coordinates.html
https://www.allaboutcircuits.com/textbook/alternating-current/chpt-2/complex-number-arithmetic/

[CRistea]

29 @ 40 degrees