
Is it possible to cut an obtuse triangle (a
triangle with one obtuse angle) into smaller triangles, all of them
acute? An acute triangle is a triangle with three acute angles. A
right angle is neither acute nor obtuse. If such a dissection can be
done, what is the smallest number of acute triangles into which any
obtuse triangle can be dissected?
The illustration shows how an obtuse triangle can be divided into
almost all acute triangles except one  the red one. Thus what
approach should be used when it is required to cut an obtuse triangle
into acute triangles only?

