What's the Tallest Place Around? Using a mirror placed on the ground, a person can determine the heights of objects that are not conveniently measured by other means. It enables one to practice with ratios and similar triangles and expand his/her ability to relate mathematics to other areas. In turn, one can determine heights of geographic landmarks in the area.
Using a mirror and similar triangles, what is the height of the flagpole in front of your school?
Select one other object. Identify the object; and using a mirror and similar triangles, how tall is it?
Using a mirror and similar triangles, what is the height of your school building at the front entrance?
Calculate - To calculate the heights of objects using similar triangles.
Compare - To compare your calculated heights with others to determine if this mirror method produces a good estimate.
Measure - To measure sides of similar triangles, using mirrors.
Supplies
A mirror (as small as a 3-inch square will work, but a larger one, such as a 12-inch square may be easier to work with)
A measuring device such as a retractable tape measure
A water soluble magic marker
A. Mark a straight line on the mirror with your water soluble marker and then place the mirror on a flat surface such as the ground, sidewalk, pavement, tabletop, etc.
B. Do not lean over to look into the mirror, but stand straight.
C. Look into the mirror and move around until you sight the top of the given object at your straight line on the mirror.
D. While you are standing in position, have a teammate measure the distance from you to the mark on the mirror and from the mark on the mirror to the object. Measure your height to your eye level.
E. Set up similar triangles, write the ratio and solve for the unknown height of the object.
See attached diagram.
A. Try this method of indirect measurement to determine the measurement of the height of the top of your chalkboard from the floor. Draw the triangles and label with measurements. Check your result with the actual measurement your teacher has.
B. Now go outside and find the height of the following familiar objects around your school. Be sure to draw traingles and indicate measurements for each. (Teacher may specify exact locations of objects on the list.)
(a) a stop sign on or near your school grounds
(b) a tree on or near your school grounds
(c) height of window on your building from ground to top of window
Compare your heights with those of the other teams to determine if your answers are good approximations of the heights.
Divide the class into teams of at least two. Have assessment photocopied and available for students before activity starts. They may have questions about the assessment that you will need to answer.You may want to provide one mirror and place it on the ground and let each team take their own measurements.The track coaches usually have tape measures that work for greater distances that they might be willing to loan to you.If you provide the materials needed other than a pencil, you will just need a day when the weather is not bad so that the students can go outside. Have the exact measurement for the top of the chalk board and if possible have any other exact measurements possible for the students to use in their comparisons. You may want to indicate which sign, which tree, and which window to use so that all measurements will be approximately the same. Discuss with the students that these indirect measures are only approximations. It might be interesting to have some of the students use the hypsometer for similar triangles in the ALCA tools and some use this mirror method and then let them do comparisons between the two methods to see which they think is the more accurate.
Duration: 1 hour
Remember this is an indirect measurement and will not produce exact results, only approximations. Be sure to draw the similar triangles and indicate the measurements on them. Write the ratio and then solve. Keep all diagrams and calculations to turn in with your assessment.
Read all materials through before you start to work on the project. You need to be aware of what will be expected and the proceudres to follow. If you have questions, direct them to your teacher for clarification.
Remember this is an indirect measurement and will not produce exact results, only approximations.
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