**Tutorial 3 Extension - Vector Addition by
Trigonometrical Rules**

### What do we do if the phasors are not at 90 degrees?

Pythagoras only works if the angles are at
90^{o}. 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 let’s 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 *V*_{1} and
*V*_{2} is 150^{o}. We use the cosine rule:

So our resultant voltage is actually 48.4 V.

Now we need to find the angle between *V*_{1} and *
V*_{R} using the sine rule. Remember to use the opposites:

That is not at all far off our initial
calculation of 18^{o}. Of course we must turn it into radians for use
in the instantaneous voltage formulae.