Trigonometry Project Student Package

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1 Trigonometry Project Student Package AWM11 Name: Date: What I can do in this unit 4-1a Label a right triangle with Opposite, Adjacent, and Hypotenuse. Level 4-1b Solve for side lengths of right triangles using the Pythagorean Theorem. 4-1c Solve for angles and lengths of right triangles using SOH CAH TOA. 4-2 Solve complex problems in the real world using right triangles. Code Value Description N Not Yet Meeting Expectations I just don t get it. MM Minimally Meeting Expectations Barely got it, I need some prompting to help solve the question. M Meeting Expectations Got it, I understand the concept without help or prompting. F Fully Meeting Expectations Strong understanding, I understand the concept without help or prompting. Almost nailed it, perhaps small mistakes or difficulty communicating methods used. E Exceeding Expectations Wow, nailed it! I can use this concept to solve problems I may have not seen in practice. I also get little details that may not be directly related to this target correct. For this project you will be working in groups of 5. I will be setting your groups. Each of you will be completing your own package (this one), but you will be working together for certain sections. You only need to make ONE clinometer per group. You will also be submitting only ONE presentation per group.

2 4-1a: I can label a right triangle with Opposite, Adjacent, and Hypotenuse. Label the following right triangles with respect to x with h (hypotenuse), o (opposite) and a (adjacent). 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)

3 4-1b: I can solve for side lengths of right triangles using the Pythagorean Theorem. Find the missing length for each using the Pythagorean theorem. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 4-1c: I can solve for angles and lengths of right triangles using SOH CAH TOA. Complete workbook p.248 #1 & 2 for angles of elevation and p. 252 #1 & 2 for angles of depression. 4-2: I can solve complex problems in the real world using right triangles. Build a clinometer using the provided info sheet. Complete the following Clinometer Worksheet (2 pages long).

4 Build a Clinometer: HOW: Create a clinometer, by following these steps. SOHCAHTOA! Carefully cut out the photocopied protractor. Glue it to your piece of cardboard. Carefully cut out the cardboard so that it is the shape of your protractor Cut a 4-inch piece of string, tape it to the middle of the protractor by your mark. It is important that you tape your string before you tape your straw. Tape your straw to the top flat end of your protractor. At the end of the string, tape a couple pennies (or nickels) to it. Your clinometer should look like this:

5 CLINOMETER WORKSHEET This worksheet will guide you through the steps necessary to use your clinometer to measure the height of any object. Answer the questions in complete sentences and in great detail. 1. Before you use the clinometer, you must understand how it works. In this project, everything you measure will be standing vertical to the ground. You will hold the straw of the clinometer to your eye and aim the straw so that you can see the very top of the object you are measuring (in the picture below it is the wall), the string line will naturally fall straight down (this is called plumb). Below is a diagram of how this will work. 2. What do you notice about the relationship between the string line and the line of the wall? 3. The picture below shows a close up version of the string line, clinometer, and line of the wall. What do you notice about the relationship between angle A and angle B? 4. What does this mean for the values of angles B and A using the knowledge you have of the relationship between the string line and line of the wall (question 2)?

6 5. Now that we have established that angles B and A will be (FILL IN THE BLANK). We can create a right triangle between your eye and the object you are measuring. For the case of measuring the height of a wall the triangle will look like this: Line XZ is the line of sight (the line you will form by aiming the straw at the corner) Line XY is the wall or the object you are measuring. Line ZY is the horizontal distance you are standing away from what you are measuring. 6. There is one side of the triangle that you can measure. Which side would it be? (XZ, XY, or ZY) 7. You can determine the measure of angle A from angle B (angle B will show on your clinometer see question 4) and from question 6 above you can measure side. With this information you can use one of your trig functions to find a measurement for side XY the vertical distance of the height of the object to the height of your eye.

7 8. On triangle XZY (taken from the picture) below label the known angle, A, the known side, d (distance), and the unknown side, h (height), that you will be solving for. 9. With this information, what trig function (cos, sin, or tan) will you use to solve for side XY. Write an equation using A, d and h as labelled above in question The final step is once you know the length of XY, adding to XY the height from your eye to the bottom of the ground. 11. Using the steps outlined above measure the height of one of your classroom walls. As you know now, you will need to measure the distance you stand from the wall, and the distance from your eye to the ground. Then you will aim the clinometer at the top corner of the wall and measure angle B (see question 4). Work together with people in your group it will be hard to read the angle on your own clinometer. 12. After you have this information complete the sketch below by putting in the correct distances and angles.

8 13. Using your measurements use the correct trig function (see question 9) and solve for the distance of side XY, and then for the height of the wall (XG). Show all your work. 14. Compare your measurement with your group members. As a group, measure the height of the wall using a measuring tape. How close were you? 15. Tree outside: We will go outside as a group and measure the tree out front.

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