Activities

• • • Subject Area

• Math: Statistics: Data Analysis
• Math: Geometry: Similarity and Proportion
• Math: Precalculus: Trigonometry (Triangle and Circular Functions)

• Author 9-12

1 Hours

• Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• TI-Navigator™
• Other Materials
Paper protractor, cardboard, straw, string, paper clip
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Finding the height of the flagpole in front of the school

Activity Overview

Students will make and use a clinometer to be able to calculate the height of the flagpole (or any tall object) in front of the school. The data from the class will be used to calculate the mean, median and compare these statistics to the actual height. I do this activity after a mini unit on trigonometry.

Before the Activity

This activity is done with students after they have studied some trigonometry. The activity will take a few partial days to complete. First, I instruct students how to make a clinometer. This is given as a homework assignment. Students will need a paper protractor, a straw, string and a paper clip. Students should cut out the paper protractor and glue it to a piece of cardboard for stability. Attach the straw so that it is on the 0? - 180? line. Attach the string with the paper clip so that it will hang at the 90? mark when held horizontally. When students look through the straw to the top of an object, the weighted string will indicate the angle of elevation.

During the Activity

Students should work with a partner. One student should stand in front of the flagpole and use their clinometer to measure the angle of elevation to the top of the flagpole. The other student should use meter sticks or tape measures to measure the distance from the student to the base of the flagpole. Because we want to compile student data, all students should measure using the same units. Students should then be able to use trigonometry to calculate the height of the flagpole. Depending on the class, you may have to remind students that the angle of elevation was found at eye level. Students will have to take this into account as they compute the actual height of the flagpole. (Students should complete questions 1 and 2 on the worksheet to record data and show their calculations.) Return to the classroom. Have students log into the TI-Navigator system. Using the Activity Center in TI-Navigator, ask students to contribute the value they calculated for the height of the flagpole (I asked students to calculate the height to the nearest tenth of a foot). Compile the data and return this to students as a list. (See Activity Center directions if needed.) Students can now use this list to calculate the mean and median of the answers received from the class. (Question #3. You can decide to have students find the mean and mean algebraically, then check answers using the functions on the calculator. Or you can have students calculate the mean and median using the calculator.)

After the Activity

After all students have completed their computations, tell students the actual height of the flagpole. Discuss the accuracy and/or possible reasons for inaccuracy in their calculations. If there are any outliers in the data, you can ask the class to speculate on why they occurred. You may decide to compute the mean and median again after omitting the outliers. You can discuss if this is a good method to find the height of an object. Students can now complete question #4 on the worksheet which asks students to write about this activity.