This task is designed to help pupils make connections between trig graphs (and the unit circle if taught this) and the application of trig in finding areas of triangles.  

I would suggest that we our ultimate aim should be to develop a culture where the pictures of the triangles would be enough for pupils to commence some form of mathematical activity.  The prompts I have bullet pointed underneath would be for the teacher to use with individuals or groups who weren’t doing anything.  This task was written with inquiry and mathematical behaviour very much at the forefront of my mind. 

Part Two aims to deepen the understanding of what is happening.  A unit circle representation and the obtuse associated rotation would help pupils to appreciate this more.  

Credit:  @chrismcgrane84