156923

Dear nrich,

My solutions are written in the attached word document.
The only question I have not provided a solution for is when the point outside of the rectangle. I was unsure on what angles I was supposed to refer to if the point results in all angles being outside the rectangle e.g. if the triangle is flipped across the vertical plain on the left side of the rectangle. However for solutions above or below the rectangle, the angle r would equal g+b - the angle of elevation or depression. If the point extends through the parallel side of the rectangle to the base angle, it can be proven in the same way as the other rectangle proofs.

Thank you for your time,
kind regards,
Lewis Arnold