Notes for Session 5, Part B

 Note 4 This activity should be conducted on level ground. It is important that the object of interest (e.g., a tree or person) and its shadow are perpendicular to each other so that the angle formed in both cases is 90 degrees. It is also important that you measure the lengths of the shadows at the same time of day. The rays of the Sun hit the tops of these objects at a specific angle, depending on the time of day, and in order for the triangles to be similar, the angles must be congruent. Note that this method only works with sunlight, and won't work with lamplight. Rays of sunlight are, for our purposes, parallel. Lamplight rays come from a point source, so they radiate. The same object will cast a different length shadow depending on its distance from the point source.

Note 5

If you are working in a group, discuss the similarities and differences between measuring shadows and using a transit to find an indirect measure. You might want to consider two important facts:

 • Similar triangles must have congruent angles. (How do we guarantee this in both cases?) • The corresponding sides must be in proportion. (How does this occur in both cases?)