Trigonometry Right Triangle Lab: Measuring Height Teacher Instructions This project will take two class parts (two days or two parts of one block). The first part is for planning and building your sighting tube; the second is for taking measurements. The goal is to measure the height of the flagpole in front of the school using two different methods: a. by measuring the angle of elevation to the top of the pole from a point on the ground b. by measuring the length of the pole s shadow Each group must have the following supplies: a long tape measure you may want to make it an assignment for students to bring in their own tape measure from home a straw a piece of thread (12-15, dark) a large paper clip or washer (to serve as a weight on the string) a pair of scissors tape a printout of the directions to make a clinometer (included in this document) a plastic protractor with a hole sunlight After the activity, each student or group must submit: a written lab report completely explaining the process diagrams with all measurements calculations for the height of the flagpole using both methods a reflection
Names: Right Triangle lab: Measuring Height: Due on Often, you need to measure indirectly, because it is not practical or possible to measure directly (Heights of mountains, heights of buildings without the building plans). A few simple measurements will allow you to measure indirectly. Your task today is to measure the height of the flagpole using two different techniques: v In the first calculation you must measure the angle of elevation to the top of the pole, and then use trig ratios to calculate the height of the pole. v In the second calculation, you must use ratios of similar triangles to find the height of the pole. Measure the shadow that the pole casts and the shadow and height of another object (or person) and set up a proportion. Needed materials: This handout. Protractor, string, straw, washer, tape that make a sighting tube. Tape measure Each group should follow these steps: 1. Use the attached directions (pg. 2) to build a sighting tube (a device to measure your angle of elevation). 2. Estimate the height of the flagpole. Record your estimation on page 3. 3. Plan how you will make the necessary calculations for both techniques. Use the worksheet on page 3 to do this. Make clear and neat diagrams and determine exactly what measurements need to be taken and who will perform each task. Measurements need to be read twice, optimally by different students to ensure accuracy. 4. Using your sighting tube, measuring tapes, plans, paper and pencils go outside and take all measurements. Your distance from the flagpole should be greater than 10 feet. This means you do not use 10 feet. 5. Record the measurements on the table on page 4. Remember to take measurements twice for accuracy. Be sure you have recorded the names of the students taking the measurements. 6. Make the necessary calculations. Record your calculations in the table on page 4. 7. Compare the results from the two different methods by answering the questions on page 4. Record your answers in the table on page 4. 8. Each student must write a paragraph reflecting on the accuracy of both techniques. Include any improvements that could have been made to improve accuracy. Write this paragraph on your own paper.
9. Make one cover sheet titled Flagpole Lab. Include the names of the group members on this cover sheet. Place the cover sheet on one packet with diagrams and calculations for both techniques along with four individual reflections. Page 1 Steps for making a sighting tube 1. Pull the string through the hole of the protractor, slide the washer onto the string, tie a knot in the string, making a loop. See image below. 2. Tape the straw as near as possible along the 0 line of the protractor. When you use the sighting tube to measure angles, hold the straw to your eye, tilt the straw up until you see the top of the object (top of the ball on the flagpole) through the straw. Use the protractor to decide the measure of the angle that you tilted through. Because our protractor measures 90 for a 0 angle of elevation you must subtract the reading on the sighting tube from 90 to get the angle of elevation that you are tilted through. Page2
Measuring Height Lab Worksheet Name A Name C Name B Name D 1. Estimate the height in feet of the flagpole. A s estimate B s estimate C s estimate D s estimate ********************************************************************************** Plan your Calculations Angle of Elevation/Trig Ratios Similar Triangles Sketch of the Situation List of Measurements needed List of who will perform each task Page 3
Height of Flagpole with Trig ratios Dist (ft.) Angle ( ) Trig Function and Work Height (ft.) 1 st measurement 2 nd measurement Average Height Average Height + your height Height of Flagpole - Similar Triangles Length of flagpole shadow 1 st measurement Length of 2 nd shadow Height of 2 nd object Proportion and Solve Height of flagpole 2 nd measurement Page 4 Average height of flagpole
Comparison of the Two Techniques 1. Are your two heights the same? Explain why or why not? 2. Why was it necessary to add your height to your answer when using the trig ratios? 3. Does it matter if the person s height is added to the average or each individual calculation? Explain. 4. Look at your original estimate. What comments can you make about your first guess and your present solution? Page 5 Individual Reflection: Do this on your own paper. Evaluate your results comparing it to the actual height of the pole. Write a few sentences explaining any major discrepancy. Discuss the accuracy of both techniques. Include any improvements that could have been made to improve accuracy.