Measuring the ImmeasurableAudience: Grade 8Main Curricular Connection: Similar Triangles

Supplies for students (per pair): 2 Laser pointers 1 Mirror Tape Measure or meter stick Dry Erase Pen or Red/Yellow Integer chip

PLOs demonstrated: demonstrate an understanding of similarity of polygons solve problems that involve rates, ratios, and proportional reasoning demonstrate an understanding of percents greater than or equal to 0% demonstrate an understanding of ratio and rate *develop and apply the Pythagorean theorem to solve problems (possible extension)

Task:Students are asked to measure the height of immeasurable objects around the school (and property) using the

mirror and laser pointers as their tools. Below are the similar triangle situations they will encounter:

The bases of both triangles can be measured and the height of the smaller triangle. That leaves the height of the larger triangle up to the student to find…We noticed that the easiest measurement was to ask the person holding the laser to tell us when the laser was on the mark and leave the integer chip as a marker for the laser. That way it can be turned off to start measurements. It is also shaky and helped improve the accuracy of the measurement. Alternatively, the mirror could be marked with a dry erase marker.

Questions: How do you know the triangles are similar? How tall is the roof, flag pole, second floor, etc.? Draw a bull’s-eye on the mirror, if you stand with the laser pointer at a height of 1m and stand 2m from the

mirror where will you place the mirror so the laser can be directed from your hand to the bull’s-eye and on to the top of the object?

Stand with your back to the wall (or any obstacle), where should you place the mirror so that it will reach the top of the object you are trying to measure (height needs to be measured first, from any position).

What is the error as a % in your measurement (vs. the actual – if known, vs. a classmates, vs. the class average,…)?

Extension (Pythagoras): How far does the laser travel?

*Requires two laser pointers (one facing forward/backward)