Part a: Most importantly, you need to recall the use of Sine Rule and apply correctly. Use calculator and tadah!

Part b: Visualise that the angle required adds up to an easily found angle with the known angle from Part a. So find that easily found angle first!

Part c: Apply Pythagoras Theorem!

Part d: Use a diagram to help you visualise how the shortest distance from A to BC will be like. It should therefore be perpendicular to BC. Find relevant angles and use trigonometry to solve.

Hope this helps!