The Broom Riddle (Solution) ft. Kurt Hugo Schneider part 3/3

In the theme of reasoning with extremes...

a,b,c are ratios of lengths of the (opposite) vertical line to some (adjacent) horizontal line. Therefore a+b>c iff it's true for some horizontal scaling (changing the "horizontal units" from cm to meters just multiplies a,b,c by 100 for example). Then let the horizontal length of each box go to zero.. now it's obvious since a,b,c each approach 90deg.