Have you ever wondered how to measure a very tall tree or a mountain or any other object that cannot be measured conveniently with a standard measuring device? We will use similar triangles, measured with either a mirror or an indirect measuring device similar to a hysometer, to construct ratios to calculate the heights of trees in your area. We can then compare these trees and their heights with those at different locations.
When might you or someone else be able to put this indirect measurement to use?
Do you think this method for determining heights of objects gives you a good estimation of the actual height of the tree?
Think about it some more. What lines of work might use this or similar measuring devices and for what purpose?
Investigate more. Are there more accurate measuring devices one might use instead of a hypsometer? What are they?
Compare Results from Different Locations - To compare your trees, heights, and growth factors to those in other regions.
Determine Growth Influences - To find and list length of growing season, average temperature, and average rainfall as factors that might influence growth of the trees.
Find Heights - To calculate the heights of trees by using similar triangles.
Use Similar Triangles - To use indirect measurement with a hypsometer type device to set up similar triangles to determine the heights of trees.
Do local Comparisons - To compare team results within a classroom to determine what to enter in the data form.
Constructing an Indirect Measuring Device
You have a choice of two different ALCA tools for measuring similar triangles. You may use this one or the one on mirrors.
Mirror, Mirror on the Ground...
You may use this ALCA tool, or the preceeding one, for measuring.
Other Supplies
Tape Measure (teacher may have one for you to use)
Calculator
A calculator may facilitate solving your ratios.
Pick either 2 or 3 below as a measuring device.
Using the ALCA tool "Constructing an Indirect Measuring Device," build something for measuring similar triangles.
Use a mirror and measurements as given in the ALCA tool "Mirror, Mirror on the Ground..."
A. Locate a tree in your neighborhood which you observe to be very tall just by looking.
B. Identify the type of tree and measure it indirectly and use similar triangles to calculate the height.
C. Find another tree of a different type which you observe to be very tall. Measure it indirectly and calculate its height with similar triangles. Try to find the tallest of this variety in your immediate area to measure.
D. Repeat this procedure for at least two more different varieties of trees so that you will have four different varieties measured.
Compare your results with those of the other teams to determine the tree(s) and heights you will enter on the Data Form. Pick the tallest of each variety to enter.
List the factors of your area which affect the heights of trees. These factors include: length of growing season; average temperature; average rainfall; and any others that you think affect the growth of trees in your area. Use the internet to assist you if you do not already have the information.
After entering your information on the data form, compare your location, tree types, heights and growth information. Do you see any similariities or differences because of location?
Divide the class into teams with a minimum of three in each. (Vary depending on size of class.)Clear your activity through the office because students will need to be off the school grounds in their local neighborhoods. If permissable with administration, teams may need to drive to various locations to take readings. Explain to your students that this is an indirect measurement and will only give an approximation of the actual height. To obtain a better degree of accuracy, the teams will need to be as percise as possible in their measurements and recordings. Provide photocopy of assessment for all of the teams. Have the teams turn in diagrams and calculations with assessment sheet. Go outside with the students to check their progress and answer their questions. Remind them to always measure their distance to the object when taking a reading before they move. Have extra measuring devices that they may use for greater distances. Not all of he teams will have access to longer measuring devices at home. (Track coach may have some he or she can loan you.) If you do not have very tall trees or if trees do not grow in your area, change the question so that students might use something such as a cactus or other species that grows very tall. When students enter the information in the data forms, remind them to specify what was measured. ASSESSMENT: Have teams turn in their data collection sheets with the influencing factors. Add a brief paragraph on comparisons.
Duration: 1 1/2 - 2 hours
Use the formula stated with your measurement device. Always draw the similar triangles to facilitate your ratios and calculations.Use a calculator for ease of calculation. Don't forget to take the measurement from the person doing the reading to the object before they move. Otherwise the reading will have to be taken again. Note the readings immediately on the data collection sheet.
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.
You may need to help your son or daughter with readings and measurements to objects.
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