Acute Dissection

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 ?

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