Concept Byte: Measuring From Afar

Use With Lesson 8-4

ACTIVITY

In this activity, you will make a tool to find heights. The tool requires you to use right triangles and trigonometric ratios.

Activity

The device shown below is an inclinometer. Make your own inclinometer using a protractor, a piece of string, and a washer.

Not to scale

1. The string on the inclinometer shows m ∠ X Y Z . m angle x y z . Explain how you can find m ∠ X m angle x if you know m ∠ X Y Z . m angle x y z .

2. You can calculate an approximate height of the tree by using a trigonometric ratio involving ∠ X . angle x .

   1. Which side length of Δ X M N cap delta x m n could you most easily measure? Explain.
   2. What trigonometric ratio would you use? Explain.
   3. Show how to find the height of the tree.

Try using your inclinometer to find the heights of tall objects at your school.

Exercises

3. You are on a steep hillside directly across from the top of a tree. Explain how you could use an inclinometer, a trigonometric ratio, and the distance from the hilltop to the base of the tree to find the approximate height of the tree.

   

   Not to scale

4. Suppose you could climb up only to point P. You know the distance, d, from P to the base of the tree. Explain how you could use an inclinometer and trigonometric ratios to find the height of the tree from P.

   

5. Use the diagram from Exercise 4. Show that you can find the height of the tree using the following formula.

   h = d ( cos b ° ) ( tan a ° + tan b ° ) h equals d open cosine b degrees close open tangent eh degrees plus tangent b degrees close

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