Right Triangle Trigonometry

Right Triangle Trigonometry

Chapter Project

Beginning the Chapter Project

How do we know how far away the sun is without stretching a tape measure across millions of miles? How do we know the mass of an electron when we can't even see one? Since ancient times, people have found ways to measure indirectly what they could not measure directly.

In your project for this chapter, you will construct an instrument similar to those used by ancient astronomers and travelers. You will use your device to measure heights you cannot easily reach. You will see how mathematics can extend your power to measure things far beyond your physical grasp.

List of Materials

· Protractor

· String

· Small, heavy object

· Meter stick or tape measure

· Straw

· Cardboard

Activities

Activity 1: Building

Use the diagram above to build a clinometer, an angle-measuring device similar to instruments used by navigators for hundreds of years. You will need a protractor, string, tape, tape measure, a piece of heavy cardboard, a small weight, and a plastic straw. Make sure that the string is aligned with the notch mark at the center of the protractor.

Bring to class on November 2.

To use the clinometer, look through the straw at the object you want to measure (the top of a building, for example). Have someone else read the angle marked by the hanging string.

· Why is the angle measure indicated by the string on the protractor the same as m∟1? (Hint: The string is always perpendicular to the horizon.)

Activity 2: Measuring

In groups, use your clinometer to measure the angle of elevation to an object such as the roof of your school or the top of a flagpole. Then determine how far away you are from the object that you measured. Use what you've learned about trigonometry to find the height of the object. Be sure to add your own height to the height you find! Each person in your group must participate.

Finishing the Chapter Project

Write a brief report explaining the variations in your estimates of the object's height. Decide as a group on a single estimate of the object's height, and defend your choice. Create a display on indirect measurement. Include the device you built and any suggestions for improving it. Also include all measurements, calculations, diagrams, and explanations from the activities in the project as well as additional measurements you made on your own.

Reflect and Revise – This will be an activity grade.

Take your clinometer home. Measure the heights of at least three objects, indirectly, using your clinometer. Create a display including all measurements, calculations, diagrams, and explanations from the activities in the project. Ask a classmate to review your project with you. Together, check that your diagrams and explanations are clear, complete, and accurate. Revise your work as needed.
Due November 9.