A uniform triangular lamina XYZ has XY=XZ and the perp. distance of X from YZ is h. Prove, through integration, that the centre of mass of the lamina is a distance 2h/3 from X.

I've done this.

A uniform triangular lamina ABC has AB=AC=5a, BC=8a and D is the centre of mass of the lamina. (Think a triangle with another triangle cut out with the same base leaving an arrow shape and the inner point of the smaller triangle being the centre of mass (see http://upload.wikimedia.org/wikipedi...w_Down.svg.png))

Worked out the centre of mass from A as 5a/3.

The plate is of mass M, has a particle of mass M attached at B. The loaded plate is suspendend from C and hangs in equilibrium.

b) Prove that in this position CB makes an angle of arctan(1/9) with the vertical.

How do I do this please?