Directions for Creating a Clinometer

Trigonome“tree” Project

We can use trigonometry to easily measure the heights of tall objects, such as trees, that would be difficult to measure directly. In this project we will be constructing a device called a clinometer to help us measure angles of elevation, thereby allowing us to use trigonometric ratios to find inaccessible heights.

You will be working with a partner on this project.

Part 1 Constructing the Clinometer

Working with a partner, follow the directions for “Constructing a clinometer on the pages 4 and 5. Be sure to follow all directions carefully to ensure the accuracy of your measurements.

1 Part 2 Measuring Heights of the Classroom Ceiling

We will be doing this part of the project in class. The first object you will be measuring is the height of the classroom. Refer to the figure below.

Record the measurements for each of the following: 1. For a, measure the distance from the floor to the student’s eyes.

2. For b, measure the distance from the student to the wall.

3. To find angle , use the clinometer. One student will sight the top of the wall through the straw and the other student will read and record the angle measurement on the protractor.

4. To find c and d you must complete the computations using trig ratios. Show all work! Include Part 2 in your final project.

2 Part 3 Measuring the Heights of Tall Objects

In this part of the project you will be using your clinometer to find the heights of tall objects, both inside the school and outdoors. For all parts of the project you must include the following: 1. A typed description of the situation. 2. A typed explanation of the setup and execution of your measurements. 3. A sketch clearly labeled and drawn to scale. (Include scale.) 4. Solutions with all computations shown.

You are required to find the heights of three objects, one must be a tree and one must be a building. For each object you will be graded using the rubric below. Scoring Rubric Score Explanation of Labeled Computations Classwork Clinometer Overall situation, setup Sketch Problem Graded Once Appearance and execution (Graded (Graded Once) (Graded Once) Once) 4 Understanding of Sketch with Complete and Figure Correct Typed and all measurement complete accurate with no complete, placement of figures neatly technique evident labeling and errors calculations protractor, straw drawn, with a scaled accurate and string, typed cover page reasonably calibrations included accurately accurate 3 One or more Sketch with Complete with Figure Incorrect Typed, figures minor concepts most things only one or two complete, placement of drawn neatly, but missing or not labeled and minor errors calculations one object, no over page mentioned scaled with only minor calibrations included or not adequately errors accurate typed

2 One key concept Sketch with Complete with Figure Incorrect Typed, figures missing missing labels key errors complete, calibrations or not drawn neatly, and/or poorly calculations incorrect cover page scaled with key errors placement of included but not objects typed 1 An attempt is Sketch Incomplete with Figure Incorrect Typed, no cover made in typed attempted, but key errors incomplete, calibrations and page included format not accurate key errors incorrect placement of objects 0 Not included Not included No computations Not included Not included Not typed Object 1 Object 2 Object 3

3 Directions for Constructing a Clinometer

Required Materials: o Drinking straw o Protractor o Metal washer o 15 cm string or dental floss o Cardboard or file folder o Glue or tape o Something to punch a small hole

Construction of the Clinometer

1. Tape a protractor to the top of a piece of cardboard or a file folder approximately 1 cm from the edge. Make sure that the edge of the protractor is parallel to the edge of the cardboard.

2. On the cardboard, recalibrate the angle measures as shown in the figure on page 5.

3. Tape a straw along the top edge of the cardboard. Make sure the straw is parallel to the top edge of the cardboard and the flat edge of the protractor.

4. Punch a small hole through the cardboard at the center of the protractor’s circular scale. (Refer to figure on next page.)

5. Insert one end of the string through the hole and tape it securely to the back of the cardboard.

6. Tie a washer to the other end of the string.

4 Clinometer

Straw Hole for string

40 40 30 30 20 20 10 10 Protractor 0

String

Washer

5 Names of Partners ______

Scoring Rubric

Score Explanation of Labeled Computations Classwork Clinometer Overall situation, setup Sketch Problem Graded Once Appearance and execution (Graded (Graded Once) (Graded Once) Once) 4 Understanding of Sketch with Complete and Figure Correct Typed and all measurement complete accurate with no complete, placement of figures neatly technique evident labeling and errors calculations protractor, straw drawn, with a scaled accurate and string, typed cover reasonably calibrations page included accurately accurate 3 One or more Sketch with Complete with Figure Incorrect Typed, figures minor concepts most things only one or two complete, placement of drawn neatly, but missing or not labeled and minor errors calculations one object, no cover page mentioned scaled with only minor calibrations included or not adequately errors accurate typed

2 One key concept Sketch with Complete with Figure Incorrect Typed, figures missing missing labels key errors complete, calibrations or not drawn neatly and/or poorly calculations incorrect or cover page scaled with key errors placement of included but not objects typed 1 An attempt is Sketch Incomplete with Figure Incorrect Typed, no cover made in typed attempted, but key errors incomplete, calibrations and page included format not accurate key errors incorrect placement of objects 0 Not included Not included No computations Not included Not included Not typed Object 1 Object 2 Object 3

Date Project Due ______10 points will be deducted for each day late!

Total Score: ______/40 points Project Grade ______