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 angles of inclination, measured with a "hypsometer," coupled with tangents of angles, to enable us to calculate the height of various trees in your area. We can then compare these trees and their heights to trees at different locations.
When might you or someone else be able to put this indirect measurement to use?
Do you think this method for determing heights of objects gives you a good estimation of the actual height of the object?
What lines of work might use this or similar measuring devices and for what purpose?
Are there more accurate measuring devices one might use instead of a hypsometer? What are they?
Do local comparisons - To compare team results within a class and to determine which tree varieties and heights to enter in the data forms.
Measure angles of inclination - To use the "hypsometer" to measure angles of inclination to the top of the trees.
Find heights - To calculate the heights of trees by using the tangent of the angle of inclination.
Do additional comparisons - To compare local 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 tress.
Assessment Sheet
Photocopied by teacher for teams.
Constructing a Hypsometer Device
Before beginning the lesson, construct the hypsometer, using this tool.
Other Supplies
Tape Measure (teacher may have some for you to use)
Calculator
Scientific Calculator
Use the the ALCA tool, found in the Required Resources, for constructing the hypsometer-type device.
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 its angle of inclination and calculate its height using the formula given with the "hypsometer" in the GeogWeb Tools.
C. Find another tree of a different type which you observe to be very tall. Measure its angle of inclination and calculate its height. 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. Be sure to select the trees of greatest height.
List the factors of your area which affect the heights of trees. Some of these factors include length of growing season, average temperature, and average rainfall. Use the internet to assist you if you do not already have the information readily available. Most local weather stations, mesonet, or TV stations have the information online for your use.
After entering your results on the Data Forms, compare your results to those in other areas. Do you see the results of the factors on the heights of trees?
Divide the class into teams that have 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. Have assessment photocopied and available for students before activity starts. They may have questions about the assessment that you will need to answer. Go outside with them 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. Remind them to measure the person's eye level from the ground for whoever takes the measurement. Have extra measuring devices that they may use for greater distances. Not all of the teams will have access to longer measuring devices at home. (Track coach may have some that he/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 they might use something such as a cactus or other species that grows very tall. When they enter the information in the data forms, remind them to specify what they have measured. Have teams turn in their assessment sheets, along with any diagrams or calculation they may have written down.
Duration: 1 1/2 - 2 hours
Use the formula: tangent of angle sighted = (Height of object - x)/distance to object where x represents the distance from the ground to the person's eye level. Use a scientific 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. If you take turns with your readings, be sure to note the distance from the ground to the person's eye level for the different people doing the readings. Be sure to keep any diagrams or calculations to turn in with assessment 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 child with readings and measurements to objects.
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