# Why doesn't the Sine or Cosine rule work when I'm resolving moments about P in this question?

I originally posted this on Physics stack exchange, but some users said it was more suited here, although the moderator who reviewed it decided not to migrate it, as it has some physics jargon- but I don't think there's too much physics involved here, just moments. To work out the resultant moment about P, I started off by working out the perpendicular distance between the 3N force and P.

To do this, I worked out the missing angles in the triangle, so in the end it looked like this: So all that is needed is to work out X, which will be the perpendicular distance, and multiply this by the 3N, which will give one moment. But when I use the sine rule, either with the 6m and 122⁰ or the 5m and 40⁰, I get different answers for X. To quickly show this:

$$\frac{6 }{\sin122^\circ} =7.08$$ $$\frac{4}{\sin40^\circ} =7.78$$

Both of the above equations should be the same, In order to work out X. I use the cosine rule, I get an answer less than 2, and from inspection alone, I know that can’t be possible.

So my conclusion is that the triangle given is not a valid triangle, as my method for resolving moments has worked for other questions. By my calculations, if $\frac{6 }{\sin122^\circ}$ is valid, then the 5m side should be 4.54m. However, I am probably missing something, so what is it that I’m doing wrong? Why couldn’t I get a valid perpendicular distance for the 3N force using the sine or cosine rule?