Students (in pairs) find the height of a large object on school property, such as a lamp pole or tree, using right angle trigonometry. The teacher then asks the students to describe multiple ways to find the height of the object using just linear distance(s) and similar triangles.
(A) One method could use the length of the shadow of the object compared to the length of the shadow of a student (see Diagram 1). Measure the length of the shadow of the student, the height of the student and the length of the shadow of the object. Have students describe how differences in the heights of the students are accounted for when they find the height of the object.
(B) A second method could use a mirror placed on the ground so that the object could be viewed by a student (see Diagram 2). Then measure the distance from the object to the mirror, mirror to the student, and height of the student. Have different groups explain how they accounted for the differences in the height of the students through the different placements of the mirrors.