Indirect Measurement

With Similar Triangles - Why does this work? Where are the similar triangles? Prove this from what you know.
Students work in groups of four: A Viewer, A Recorder & 2 Measurersshadow diagram.jpg
You will need 100' measuring tapes, a calculator, and tall objects to measure.
If using shadows outside, try this.
1.) The viewer stands a little away from the object in question.
2.) The measurers measure the length of the viewer's shadow(V).
3.) The recorder writes the measurement as V.
4.) The measurers measure the length of the object's shadow (S).
5.) The recorder writes the measurement as S.
6.) The measurers measure the height of the viewer (H).
7.) The recorder writes the measurement as H.

What? Can't go outside? No problem - Try the activity with mirrors. Why does this work? Where are the similar triangles? Prove this from what you know.
1.) Find the object to measure.MirrorDiagram.jpg
2.) The viewer will stand behind and look down at the mirror, moving around until the top edge of the object is viewed at the edge of the mirror.
3.) The measurers will measure the distance from the viewer's eyes to the ground. Be sure you measure perpendicular to the ground!!!!
4.) The recorder writes the measurement as d.
5.) The measurers measure the distance from the viewer to the mirror.
6.) The recorder writes the measurement as f.
7.) The measurers measure the distance from the mirror to the object in question.
8.) The recorder writes the measurement as w.

Here's a downloadable worksheet
as a Word Document
as a .PDF

With TRIG -
When teaching geometry and doing the chapter on trig, students would encounter problems with a triangle, one side and one angle given,Indirect Measurement.png and they had to find another side, often the height of a building or tree. What I found is that they could do it in the book but when I took them outside, the "question in the book" became a real "problem" real with real challenges and required them to think more deeply into what they had to do.
  • After doing the problems in the book, give them something outside to find the height of. Don't give them step-by-step directions. Let them problem solve.
  • Divide the students into teams of 3-4 students, give each group a 100' tape measure, clinometer, calculator, paper, and pencil, they set out to find the height of a building, the height of a lamp post in the parking lot, or other tall objects available. Going outside and doing "real life" problems seem to be motivating for most students.
  • Tip: Show them how to use a clinometer and make sure that they look at their measuring tapes and find the "zero" and can read the measures. I have found that even high school students need to go over this - they don't do it much anymore at home! Take the time to do this.
  • After doing the problems in the book, give them something outside to find the height of. Don't give them step by step directions. Let them problem solve. (See CCSS Math Practice #1)