Measuring Tall Objects: A Historical Perspective
Measuring any tall object is a difficult task. In modern times, we have sophisticated measuring
devices that allow us to find the height of a tall object. In 3000 B.C., however, this was a much harder
problem. The Chinese used similar triangles to find the height of tall objects, and you will be modeling
this ancient Chinese practice.
The Chinese used what was called a gnomon. A gnomon is a straight stick of known size. Using
the gnomon, the Chinese were able to create a shadow and then form a proportion with the shadow of
the object they were trying to measure. Since the angle of the sun casts shadows at the same angles for
all objects, the gnomon and the tall object create similar right triangles.
Similar Triangles Geometry Project
Your task is to find a tall object somewhere in Dublin and use “geometry” to measure it. The
object must be at least 10 ft tall. The object cannot be a basketball hoop or a street sign. Be careful
about choosing an object that has rounded top. You will need a measuring tape to measure the shadow
of the object you choose and the shadow of your gnomon. Make sure there’s no bend in the shadow.
Have your partner measure your shadow to create the similar right triangles. The measurements must be
made at the same time so the angle of the sun is the same. Record all measurements for use in your
project. Label them in feet, inches, meters, depending on what measure is on your measuring tape.
Your partner is only there to help you with the measurement, not to use the same object
for his/her project!
To complete the project:
1. Make a sketch of the scene you measured including the shadows. Use stick people if necessary. Be
sure to label each part with descriptions and measurements.
2. Make an exact scale drawing of your triangles on graph paper. Include a scale factor for the
drawing. On the same graph paper, show the calculation used to find the unknown height.
3. Type a paragraph to summarize your work. Tell the name of the tall object, where it is
located(address or cross-streets) and who was your measuring partner. Include information about
the process you used to measure the shadows and the gnomon. Include some fact(s) you know
about similar triangles that justify your calculation. Be sure to conclude with the calculated value of
the height of the tall object.
4. Take a camera along and ask someone to photograph you conducting the measurements. You may
attach one or two photos that show the object, its shadow, you, and your shadow. This can be a
digital image or a photo image.
Keep this paper clean and flat. Return it with your completed project