Resolution of horizontal forces about oblique axis I am facing problem in resolution of moment. Here is the question along with my attempt at solution.

I have always resolved forces and moments by using trigonometry. But here, when i use trigonometry to determine moment along Y-axis , i get √2 Mx ; whereas the answer is Mx/√2 . A friend of mine told me to use Lahmi's theorem to determine My and it does give the correct answer i.e Mx/√2 . So, why doesn't trigonometry give me the same result. Please tell me where i am going wrong.
 A: Trigonometry will work here. The problem is that seem to project the force $M_y$ onto the direction $\hat x$. For this case, he answer will be correct.
In your case, you want to project the other way around. So the right angle is at the wrong position, the green light should be the hypotenuse. Then the roles are inverted and you get the factor $1/\sqrt{2}$ instead of $\sqrt{2}$ you want.
See the following illustration. On the right I have reproduced your angles, What happens there is that the vector $M_y$ is projected down on the $\hat x$ direction. Therefore the right angle is at the $\hat x$ axis. The trigonometry gives you the relation you got. On the left, I have projected $M_x$ onto the $\hat y$ direction. the right angle is always on the axis where you project to, so the roles of base and hypotenuse are exchanged, effectively giving you the $\sqrt 2$ on the other side of the equation.

The general rule is that the right angle is formed between the axis you project upon and the dotted line connecting the previous arrow head with the new one.
