This is a fantastic way to layout this problem posted on twitter by Olivier Longuet and pointed out to me by Ralph Pantozzi. The drawing progression is on the right or you can etch the left (blank) onto wood, and add the finished pieces as you figure it out. Our files are here if you want a jpg, svg, Corel or AI file.
By the power of the rectangle- opposite sides are equal, we can get that the left side= right side means sin (a+b) = cos a sin b + sin a cos b
the top = bottom means cos (a + b) = cos a cos b – sin a sin b
Using the drawing progression on the right you can make a variety of versions as long as the center triangle touches all the sides and has a right angle. Set up your labels this same way and the proof will follow regardless of the angles and side lengths. Each student can make their own unique version : )