A hypsometer-type device can be made and used to set up similar triangles to find unknown heights (altitudes) of objects such as trees, poles, buildings, or any physical geographic characteristics of your locale.
Select one other object. Identify the object and tell how tall it is.
What is the height of your school building at the front entrance?
Using your hypsometer, what is the height of the flagpole in front of your school?
If there are any trees on you school grounds, what is the height of the tallest tree? If there are no trees, but there are large succulents, how tall is the tallest?
Solve -The learner will construct an indirect measuring device to use with similar triangles to solve for unknown heights(altitudes) of objects.
Supplies
Heavy cardboard 5-in by 10-in; drinking straw at least 10 inches long;12-in string; small weight, such as a paper clip.
Other Supplies
Marking pen;metric ruler or standard ruler;metric or standard tape measure;tape;scissors.
Gather the following materials:
Heavy piece of cardboard 5-in by 10-in
Drinking straw
12-in string
Small weight such as a paper clip
Marking pen
Tape
Mark off 1/2-in increments on one of the 5-in sides and on one of the 10-in sides of the cardboard. Number 1-10 on the 5-in side and 1-20 on the 10-in side. Be sure the two marked sides are adjacent and that the numbers 1 are adjacent. Again, there will be 10 spaces on the 5-in side and 20 spaces on the 10-in side when you have finished marking.
Attach the straw with tape to the longer side of the cardboard, the one that you did not mark off in increments. With scissors, trim the straw to the length of the cardboard.Tie the small weight to one end of the string and attach the other end of the string to one end of the straw next to a marked side as shown in the diagram. Again, tape will work(SEE ATTACHED DIAGRAM).
Sight through the straw to the top of the object. Note where the free-hanging string crosses the scale on the side marked with 1-20 (10-in side) and record this measure to the nearest numbered increment. This will set up a right triangle with one leg of 10 and the other leg as read from the measurement.Measure the distance from the base of the object whose height you are finding, to where you stand when you take the reading and record. Measure the height from the ground to the eye level of the person doing the sighting. Use the formula shown with the diagram to calculate. (SEE DIAGRAM ATTACHED ABOVE) Do some trials on various objects and compare within your group. Be sure to make a diagram of the similar triangles to aid you in identifying the corresponding sides and angles.Set up a similar triangle ratio and solve for the height of the object.
Use your team's device to use indirect measurement and similar triangles and the formula to find (1) the height of the top of the chalkboard from the floor in your classroom and (2) the height of the tip of the Ameriacan flagpole from the floor in your classroom.Compare your heights to the actual heights the teacher has already measured with a tape measure. Is the height you found a good approximation of the actual height?
You may want to convert the measurement to centimeters instead of inches.Have assessment photocopied and available for students before activity starts. They may have questions about the assessment that you will need to answer.Have a measuring device that will measure the distances from the students to the object being measured. More than one would facilitate your time factor. The track coach may have some tapes used to measure for shot and discus that would not restrict the student's distance to the object as much. Carpenters retractable tape measures will also work, but you will at times be restricted by their length. A measuring cord could be developed by tying knots at consistent intervals such as meters, feet, or yards. Some of the students may have them at home and be willing to bring them to use in their measurements. Measure the actual height of the top of the blackboard and the tip of the American flagpole from the floor so that the students can compare their indirect measurement with the actual measurement. It might be interesting to have some of the students use the hypsometer for similar triangles in the ALCA Tools and some use the mirrors in ALCA Tools and then let them do comparisons between the two methods to see which they think is the more accurate. (These can be found in a search of "hypsometer" and "mirror.") Remember, this is an indirect measurement and will not produce exact results, only approximations.
Duration: 1 hour
Assemble "hypsometer" as directed. Make sure the string hangs freely to create a plumb line. Sight through the straw to the top of the object being measured. Note where the string crosses the scale. Use similar triangles to find the height of the object. SEE DIAGRAM. To use similar triangles, you will have to measure the distance from the base of the object to where you stand when you use the "hypsometer" and record that distance. Sketch a diagram of the similar triangles created by the "hypsometer" and the object to help you analyze the ratios needed. Add in the height of the person (X) using the "hypsometer" to the height of the object, (H) unless you lie flat to do the measurement. Remember, this is an indirect measurement and will not produce exact results, only approximations.
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 student with the measurement of the distance from the person measuring, to the object being measured and with the reading, if they are working alone. Have some items for them to measure with the hypsometer and similar triangles and then measure the actual height of these objects so that the student can compare their indirect measurement with the actual measurement. You will need a tape measure that is capable of measuring several meters and or feet in distance. Remember, this is an indirect measurement and will not produce exact results, only approximations.
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