For the laser beam to be reflected into the detector, the mirror's normal should make an angle of approximately 89.174 degrees with due south after proper alignment.
In an experiment designed to measure the speed of light, if a laser is aimed at a mirror 57 km due north and a detector is placed 205 m due east of the laser, the mirror should be aligned in such a way that the angle of reflection equals the angle of incidence. We can visualize this situation by imagining a right-angled triangle where the path of the light to the mirror and back to the detector forms the hypotenuse, with the distance between the laser and the detector forming the other two sides of the triangle.
When the mirror is properly aligned, the normal to the surface of the mirror should make an angle with due south which is equal to the angle of incidence. This angle can be found using trigonometry, specifically by calculating the arctangent (arctan) of the opposite side (205 m) over the adjacent side (57,000 m), and then doubling that angle since the light reflects off the mirror at the same angle it arrives. This yields an angle of approximately 0.413 degrees. Dobuled, the alignment angle with respect to due north (incident angle) is about 0.826 degrees, and therefore the angle with respect to due south (the normal to the mirror) should be 90 - 0.826 degrees, which is approximately 89.174 degrees.