Tutorial 3 Extension - Vector Addition by Trigonometrical Rules
Pythagoras only works if the angles are at 90o. We can do the easier method of resolving vectors and adding the components. However we can also use some mathematical rules as shown here. If you have a mathematical aptitude (which I do not), you may prefer to use this approach.
So letís go back to our first situation and use our original voltage vectors and the original phase angle:
We can redraw the vectors as a closed triangle.
We can see easily that the angle between V1 and V2 is 150o. We use the cosine rule:
So our resultant voltage is actually 48.4 V.
Now we need to find the angle between V1 and VR using the sine rule. Remember to use the opposites:
That is not at all far off our initial calculation of 18o. Of course we must turn it into radians for use in the instantaneous voltage formulae.