A block of mass 50kg resting on a rough surface with a coefficient of friction equal to 1/3. Find the maximum angle at which the surface can be inclined to the horizontal without the block slipping. Give your answer to 3 significant figures

Break the solution down into small logical steps, outlining thought process in each one to make it clear to the examiner what it is you are try to do. Emphasise the importance of a clear and neat layout of the tutees working.
1) Draw a large Free Body Diagram showing a block resting on an inclined plane at an angle alpha. Draw on the forces for the Weight acting vertically down from the centre of the block, the normal reaction force acting perpendicular to the inclined plane from the centre of the block, and the Friction force acting parallel to the inclined plane pointing up the slope. Add details such as the coefficient of friction to the diagram for ease later in the question.
2) Resolve forces according to Newton's Second Law perpendicular to the inclined plane as to eliminate friction and to obtain a value for the Normal Reaction in terms the Weight and alpha. In this example: R - 50gcosa = 0, therefore R = 50gcosa
3) Use the equation for Friction to find friction as the product of the coefficient of friction and the normal reaction. F=uR, therefore F = (50gcosa)/3
4) Resolve forces parallel to the inclined plane and set equal to zero (for equilibrium to be maintained)50gsina - (50gcosa)/3 = 0, therefore sina = (cosa)/3
5) Solve the equation for alphatan a = 1/3therefore a = 18.4 degrees (3sf)