The geometric construction of the $90^\circ, 87^\circ, 3^\circ$ triangle The construction of the $90^\circ, 45^\circ, 45^\circ$ and the $90^\circ, 60^\circ, 30^\circ$ triangles is well known. 
How can be constructed a triangle with angles $90^\circ, 87^\circ, 3^\circ$ without using regular polygons? By "construction" I mean the determination of the proportion of its sides and the required internal angles by the common operations in plane geometry, like in the other triangles.
Is it possible to use the exterior angle theorem and the triangles $90^\circ, 72^\circ, 18^\circ$ and $90^\circ, 75^\circ, 15^\circ$ to construct geometrically the angle $18^\circ - 15^\circ= 3^\circ$? How this construction can be done?

A hint: $3^\circ=45^\circ+30^\circ-72^\circ$. For $72^\circ$ however you have to know how to construct a regular pentagon or some golden ratio triangle.
