for A, B, C being Point of (TOP-REAL 2) st A,C,B is_a_triangle & angle (A,C,B) < PI & |((A - C),(A - B))| <> 0 holds
the_length_of_the_altitude (C,A,B) = |.(A - B).| * |.(((sin (angle (C,B,A))) / (sin ((angle (B,A,C)) + (angle (C,B,A))))) * (sin (angle (C,A,(the_foot_of_the_altitude (C,A,B)))))).|