The teacher places the mirror at point C, a distance ds away from the student (see picture). She then steps away from the mirror until she sees the top of the student's head in the mirror. Let's call the distance from the teacher to the mirror dt. The teacher knows her height, ht, and she knows that the angle of incidence equals the angle of reflection when a beam of light hits a reflective surface. We call this angle ß. Since the triangles ABC and DEC are right triangles and since they share the angle ß, they are similar. So the teacher knows that, once she measures dt and ds, by similarity of the two triangles, she can say that ht/dt = hs/ds or hs = (ht ds)/dt. In other words, by knowing her own height, and by measuring her own as well as the student's distance from the mirror, she can calculate the student's height.
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