This hypsometer-type device can be used to measure angles of inclination to an object. Using trigonometric ratios, the heights of objects such as trees, poles, buildings, and other geographic landmakrs can be found.
Using your hypsometer, read the angle of inclination of your school's flagpole. Using your formula, what is the height of the flagpole?
If there are trees on your school grounds, what is the height of the tallest tree?
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?
Measurement - To measure angles of inclination using a hypsometer.
Construction - To construct a hypsometer that measures angles of inclination.
Calculation - To measure angle of inclination, distance from object, and distance from eye level to ground, using the resulting formula to calculate heights of given objects.
Materials
Heavy piece of cardboard about 5-in by 7-in. (a 5x7 index card will work);tape;straw;photocopy of protractor;string;paper clip or small weight;magic marker;paste; and tape measure for longer distances.
Calculator
Scientific calculator is helpful. If one is not available, use the trigonometric tables found in most higher level math books.
Assemble 5 x 7 index card, tape, straw, photocopy of protractor, string, paper clip and scientific calculator.(ATTACH PROTRACTOR)
A. Cut protractor from photocopy.B. Glue or paste protractor to heavy cardboard. C. Cut straw to fit top of cardboard.
D. Attach straw to top edge of cardboad with tape along entire edge.E. Tie the paper clip to one end of the string.F. Attach the other end of the string to the center point of the protractor. G. Be sure all parts are firmly attached and glue or paste is set. H. Color string with magic marker to make it easier to read.(Attachment of diagram)
Take turns practicing finding a horizontal line of sight and measuring angles of inclination. Compare your results to others in your group.A. Use the hypsometer to sight the top of the object being measured through the straw and have another team member record the angle (to the nearest degree) where the string crosses the hypsometer for the ceiling in your classroom in a corner. This will give you an angle of inclination.B. Measure the ground distance from the person doing the measurement to the object being measured and record.C. Measure the distance from the eye-level to the ground for the person doing the reading for the angle of inclination and record. D. Repeat this process A-C for the top of the chalkboard.
Use a scientific calculator and the following equation to solve for the heights of the ceiling and the chalkboard in your classroom using the data gathered in Step 3 above. tan (angle sighted) = (height of object - x)/distance to object where x represents the distance from the ground to the person's eye level.(SEE DIAGRAM)
Compare your results to the actual height of the ceiling and the chalkboard, which have been premeasured by your teacher.
Divide the students into teams. A minimum of two people to a team is necessary so that one can do the sighting and the other can note the reading.If students are to supply their own materials, assign teams and supply list 2-3 days ahead of date scheduled for tool construction. Allow them to have 3-5 minutes to decide who will bring what on the supply list.If you or your students have protractors, they can be taped to the cardboard instead of a photocopy of a protractor.Have measuring tape(s) for the students to use to take their distance measurements.The track coach may have some tapes used to measure shot or discus that he would loan you. Some of your students may be able to bring one from home. If necessary, a measuring cord may be made by tying knots at convenient intervals such as meters, feet, or yards. You may be limited by the length of your measuring devices. Remind them to bring supplies on the day before the construction.Have assessment photocopied and available for students before activity starts. They may have questions about the assessment that you will need to answer.Have the protractor photocopied unless you prefer to use an actual protractor. In that case, the student will need to supply the protractor or you the teacher will need to supply them. Also this would require them to subtract the reading from 90 degrees in order to have the angle of inclination.Once the hypsometer is constructed, make sure they take turns practicing so they will all know how to read the hypsometer.Build an example for the students to look at during their construction and then demonstrate how to look through the straw to cite the top of an object and then to take the data readings.Check the students to be sure they are doing the readings correctly.If your students do not use scientific calculators or do not have access to them, be sure they have a table of trigonometric ratios to follow to look up the tangent of their angles. More time will need to be allowed if they use the tables.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. Practice finding a horizontal line of sight and reading hypsometer for angle of inclination.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.
A plastic or metal protractor, rather than the paper photocopy, may be used to attach to the cardboard.Remember, this is an indirect measurement and will not produce exact results, only approximations.
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