A rectangular block has a height of 20cm and a square base of side 10 cm. It is placed with its square base on a rectangular board . When the board is tilted about one edge, it makes an angle A with the horizontal when the block is at the point of toppling over . Find the value of A.

The center of mass of the block would be at the center of the block assuming it to be made of an homogenous material. So the center of mass would be a point originating 5cm within the side of the block and 10cm within from the top.

You just calculate the angle at which the horizontal component of the normal force creates a moment about the bottom edge of the block that is greater than the moment created by the vertical component of the normal force.

Simple as that.