 ## Using Trig in the Real World

A WebQuest for 9th Grade Algebra

Designed by

Shannon (Hosier) Mersand
mersands@pawlingschools.org Introduction

Last class you learned how to convert between angles and sine, cosine and tangent using a trigonometric table and your calculator. As with many things you learn in math, I bet you wonder just when you are going to need to use this in your life? It's hard to believe that all of those letters and formulas will come in handy some day, but they will!

In this quest, it is your responsibility to learn about Trigonometry (Pythagorean Theorem, and the Trig Ratios for Sine, Cosine and Tangent) and how it can be applied in the "real" world. You will combine your previous knowledge with what you learn over the next few days. You will then prepare a presentation for the incoming freshmen that explains the basics of Trigonometry and how they can apply it to their summer jobs. The Task

At the completion of this webquest, you will be able to explain basic trigonometry concepts and how to use them in a summer job.

• Task 1: Individually, familiarize yourself with Trigonometry, the Pythagorean Theorem, and the Trig Ratios. You will need these basics to help you describe the real world application of trigonometry.
• Task 2: Individually, read the examples provided of how trigonometry is used every day.
• Task 3: In your assigned group, each of you select one summer job from the list. Each job has related tasks with it. You must brainstorm how to use the basic trigonometry ratios and theorem to accomplish the tasks.
• Task 4: Create a PowerPoint Presentation with your group mates to educate the incoming freshmen about trigonometry and how it can be applied to their summer job. Specific requirements are listed below. The Process

#### Task 1:

Read through the following links to familiarize yourself with trigonometry. Take notes for later use on each of the ratios and theorem, including sketches and formulas. Please note, your notes will be both useful later, and graded. Copy and paste into a Word document does not constitute note taking. You must take these notes by hand.

Make sure to answer the following questions in your notes:

1. What is Trigonometry?
2. What is the Pythagorean Theorem?
3. What are the Trig Ratios?

Your Resources:

• Drexel University. (1996, August 20) Ask Dr. Math: What is Trigonometry. Retrieved April 13, 2008 from Math Forum: http://mathforum.org/library/drmath/view/54003.html
• Definition of Pythagoras Theorem. (2007, November 26). Retrieved April 13, 2008 from Math is Fun: http://www.mathsisfun.com/definitions/pythagoras-theorem.html
• Geometry and Trigonometry Reference Area. (c2007) Retrieved April 13, 2008 from Cool Math: http://www.coolmath.com/reference/geometry-trigonometry-reference.html
• Maths First. (2006, August 9). Trigonometry Index, Maths First, Institute of Fundamental Sciences, Massey University. Retrieved April 13, 2008, from Massey University: http://mathsfirst.massey.ac.nz/Trig.htm
• Oswego City School District. (c2008) Pythagorean Theorem. Retrieved April 17, 2008 from Regents Prep: http://www.regentsprep.org/Regents/math/ALGEBRA/AT1/Pythag.htm
• Oswego City School District. (c2008) Right Triangle Trigonometry: Solving for a side. Retrieved April 17, 2008 from Regents Prep: http://www.regentsprep.org/Regents/math/ALGEBRA/AT2/Ltrig.htm
• Oswego City School District. (c2008) Right Triangle Trigonometry: Solving for an angle. Retrieved April 17, 2008 from Regents Prep: http://www.regentsprep.org/Regents/math/ALGEBRA/AT2/LtrigA.htm
• #### Task 2:

Individually, read the two examples provided of how trigonometry is used every day. Take notes on the line of work and the Trigonometric theorem or function used. Please remember, your notes will be both useful later, and graded. Copy and paste into a Word document does not constitute note taking. You must take these notes by hand.

Make sure to answer the following questions in your notes:

1. What is the line of work?
2. Which theorem or ratio did they use?
3. Provide a sketch of how the answer was found

Your Resources:

• Cooper, M. (2005, November 22) Conviction With an Angle Is Upheld by Court of Appeals. The New York Times. Retrieved April 13, 2008, from: http://www.nytimes.com/2005/11/23/nyregion/23drugs.html
• Eisenberg, J. D. (2006). Trigonometry - Surveying Uses. Retrieved April 17, 2008 from Cat Code: http://catcode.com/trig/trig13.html
• #### Task 3:

Arrange yourselves into groups of three (3). In your group, discuss and brainstorm how to solve each of the tasks using the basic trigonometry functions you just learned. Using the list of available jobs and tasks from each, you must apply each of the trigonomic ideas you learned about in this quest to the jobs. Brainstorming should be done on paper, as your note taking was, and you may not search the internet for ideas. Each group member must take their own notes and show evidence that they participated in the discussion.

Make sure to answer the following questions in your notes:

1. Your job
2. The task
3. The Theorem or Ratio
4. The solution

Your Employment Prospects:

• Landscape Helper
1. The land to be mowed today is in the shape of three squares with a right triangle shaped house in the middle. Side a and b are the legs, side c is the hypotenuse. Without knowing the length of any of the sides, you have a choice of which parts to mow. You can mow either the square in front of side c, or the two smaller squares on sides a and b. Which is your choice? Does it make a difference? Justify your answer.
2. The owner of the triangle house would like to plant a garden on the corner where lawns A and B meet. There is a gate on lawn A which sits 3 feet from the corner of the house. The garden should meet the gate, and the farthest corner of Lawn B. You have an 8 foot board to use as a barrier for the garden. At what angle will the board meet lawn B to meet all of the requirements?
3. After creating the corner garden, you need to decide what plants will grow best based on the amount of sunlight it receives. You put a 3 foot tall stick in the center of the hypotenuse of the garden, and the shadow of the stick measures 2 feet at 12 noon, when the sun is at it's highest point in the sky. What is the angle of the sun above the horizon (angle on ground)? Direct sun plants grow best when the angle of the sun is 67 degrees or more, partial sun when it is between 34 and 66 degrees and shade plants grow best when the sun is at 33 degrees or less. Which plants will grow best, ones that need direct sun, shade plants or partial sun?
4. In order to get mulch into a raised flower bed, you need to build a ramp. The bed is 3 feet off the ground, and you want the incline of the ramp to 9 degrees so the wheel barrow is easier to push. How long should you make the ramp?
• Janitor's Helper
1. You have to install wires in the ceiling to run internet in the elementary school. There is a limited amount of wire for the entire building, so you need to use as little as possible. The room you are currently going to wire is 20 by 23 feet. What is the least amount of wire you can use to wire the ceiling in this room?
2. The Janitors need to install a new flag pole which should be the same height as the existing pole, but they don't know how tall the existing pole is. You walk 100 feet from the pole and measure the angle at which you can site the top of the pole from the ground. This angle is 37 degrees. How tall should the new flag pole be?
3. After the janitors install the pole, it won't stand against the wind and they want you to figure out how long to make a support cable that will extend from the top of the pole to the ground. They want the angle of the cable to be 75 degress. How long should the cable be? How far away from the pole should you put the anchor?
4. Your last job as a janitor's helper it to fly a helium balloon to welcome the new freshmen to school in the fall. You should support it with 3 strings, one on each side, and one in the middle. You can attach the side strings on either side of the building, 50 feet on each side from the center and you can use 100 feet of string on each side. What angle will the string attach to the building at assuming the balloon flies as high as it possibly can? How long should the center string be to allow the balloon it's maximum height?
• Carpenters helper
1. You have to make a brace for a door that is wobbly. You are going to use a diagonal wire brace. The door is 8 feet high and 3 feet wide. How long should the brace be to make sure the corners of the door remain square.
2. You have to help the carpenter decide how long to cut the boards to make a roof. You know that the angles where the sides meet at the top is 90 degrees, that the angle where they meet the house has to be equal, and the width of the house is 8 yards. At what angle does the roof meet the side of the house and how long should each side of the roof be?
3. You need to help design a handicap ramp for a new office building. By law, the ramp needs to have a 7 degree incline (meet the ground at 7 degrees) and the porch it leads up to is 3 feet above the ground. How far will the ramp extend from the building? How long should the ramp be?
4. Your boss forgot his tape measure today, but you need to install molding in a triangular room in which one corner is 90 degrees. The wall opposite the 90 degree angle is the same length as your 10 foot ladder. Yesterday, the carpenter measured one corner to be 63 degrees. How long should you cut the other two pieces of molding? How wide is the other corner?
• Sales Clerk
1. A customer comes in and wants help replacing their old computer monitor. She says the current monitor they own is 5 inches high by 15 inches wide. Since monitor size is actually decided by how long the diagonal is from one corner to the other, what size screen would you recommend they purchase?
2. A customer wants buy a corner desk that extends 10 foot on one side, and 4 foot on the other. The desk is going into a room where the end of 10 foot section must fit into a corner that has an angle of 23 degrees because of a door that opens into the area. Will this desk fit in the designated area?
3. A customer wants to put a tarp up to serve as an awning over his deck. To make sure things stay dry, he wants to attach it at a 39 degree angle to the deck rail. The deck he wants to cover is 10 feet wide. What is the smallest tarp he can purchase to meet his needs?
4. A customer wants to put a bookshelf in an alcove where the roof meets the floor at a 54 degree angle. She wants to put the shelf 3 feet from where the wall and ceiling meet. How tall of a bookshelf should she buy?

Your Resources

• Spector, L. (c2008) Three-place Trigonometry Table. Retrieved April 20, 2008 from The Math Page: http://www.themathpage.com/aTrig/trigonometric-table.htm
• #### Task 4:

Using your notes, create a PowerPoint Presentation with your group mates for the incoming Freshmen that explains Trigonometry and how they can use it in their summer jobs.

Be sure that your PowerPoint contains the following information:

1. Identification Information
1. Your name(s)
2. Your Teacher's Name
3. Your Class period
2. Definition of Trigonometry
3. Pythagorean Theorem
1. The formula
2. A diagram
3. When it is applied
4. Summer job task(s) with solutions
4. Trig Ratios (Sine)
1. The formula
2. A diagram
3. When it is applied
4. Summer job task(s) with solutions
5. Trig Ratios (Cosine)
1. The formula
2. A diagram
3. When it is applied
4. Summer job task(s) with solutions
6. Trig Ratios (Tangent)
1. The formula
2. A diagram
3. When it is applied
4. Summer job task(s) with solutions

PLEASE NOTE:

Diagrams may be taken from the internet, but you MUST download the image, not copy and paste it and you MUST say where they came from (remember, Google is not a source, it is a tool, you must provide the web address of the actual website that contains the image). Evaluation

You will recieve one total grade for this project, with part of the points coming from your notes and the other part from the PowerPoint Presentation.

 Beginning 0 Developing1 Accomplished2 Exemplary3 In Your Notes Define Trigonometry No definition of Trigonometry Vague definition of Trigonometry Mostly accurate definition of Trigonometry Accurate definition of Trigonometry Explain the Pythagorean Theorem using the formula and a sketch No explanation, formula or sketch of the Pythagorean Theorem Errors in explanation of the Pythagorean Theorem OR missing the formula and a sketch Some errors in explanation of the Pythagorean Theorem OR missing the formula or a sketch Accurate explanation of the Pythagorean Theorem using the formula and a sketch Explain the Trig Ratio (Sine) using the formula and a sketch No explanation, formula or sketch of the Trig Ratio (Sine) Errors in explanation of the Trig Ratio (Sine) OR missing the formula and a sketch Some errors in explanation of the Trig Ratio (Sine) OR missing the formula or a sketch Accurate explanation of the Trig Ratio (Sine) using the formula and a sketch Explain the Trig Ratio (Cosine) using the formula and a sketch No explanation, formula or sketch of the Trig Ratio (Cosine) Errors in explanation of the Trig Ratio (Cosine) OR missing the formula and a sketch Some errors in explanation of the Trig Ratio (Cosine) OR missing the formula or a sketch Accurate explanation of the Trig Ratio (Cosine) using the formula and a sketch Explain the Trig Ratio (Tangent) using the formula and a sketch No explanation, formula or sketch of the Trig Ratio (Tangent) Errors in explanation of the Trig Ratio (Tangent) OR missing the formula and a sketch Some errors in explanation of the Trig Ratio (Tangent) OR missing the formula or a sketch Accurate explanation of the Trig Ratio (Tangent) using the formula and a sketch Identify line of work AND theorem or ratio used AND a sketch of the answer for example 1 Did not identify line of work, theorem or ratio used or a sketch of the answer for example 1 Identify 1 of: line of work; theorem or ratio used; a sketch of the answer for example 1 Identify 2 of: line of work; theorem or ratio used; a sketch of the answer for example 1 Identify line of work AND theorem or ratio used AND a sketch of the answer for example 1 Identify line of work AND theorem or ratio used AND a sketch of the answer for example 2 Did not identify line of work, theorem or ratio used or a sketch of the answer for example2 Identify 1 of: line of work; theorem or ratio used; a sketch of the answer for example 2 Identify 2 of: line of work; theorem or ratio used; a sketch of the answer for example 2 Identify line of work AND theorem or ratio used AND a sketch of the answer for example 2 Identify summer job, task, theorem or ratio AND solution for task 1 Did not identify summer job, task, theorem or ratio OR solution for task 1 Identify 2 of: summer job, task, theorem or ratio OR solution for task 1 Identify 3 of: summer job, task, theorem or ratio OR solution for task 1 Identify summer job, task, theorem or ratio AND solution for task 1 Identify summer job, task, theorem or ratio AND solution for task 2 Did not identify summer job, task, theorem or ratio OR solution for task 2 Identify 2 of: summer job, task, theorem or ratio OR solution for task 2 Identify 3 of: summer job, task, theorem or ratio OR solution for task 2 Identify summer job, task, theorem or ratio AND solution for task 2 Identify summer job, task, theorem or ratio AND solution for task 3 Did not identify summer job, task, theorem or ratio OR solution for task 3 Identify 2 of: summer job, task, theorem or ratio OR solution for task 3 Identify 3 of: summer job, task, theorem or ratio OR solution for task 3 Identify summer job, task, theorem or ratio AND solution for task 3 Identify summer job, task, theorem or ratio AND solution for task 4 Did not identify summer job, task, theorem or ratio OR solution for task 4 Identify 2 of: summer job, task, theorem or ratio OR solution for task 4 Identify 3 of: summer job, task, theorem or ratio OR solution for task 4 Identify summer job, task, theorem or ratio AND solution for task 4 Notes Score In Your PowerPoint Define Trigonometry No definition of Trigonometry Vague definition of Trigonometry Mostly accurate definition of Trigonometry Accurate definition of Trigonometry Explain the Pythagorean Theorem using the formula and a sketch No explanation, formula or sketch of the Pythagorean Theorem Errors in explanation of the Pythagorean Theorem OR missing the formula and a sketch Some errors in explanation of the Pythagorean Theorem OR missing the formula or a sketch Accurate explanation of the Pythagorean Theorem using the formula and a sketch Identify when to use the Pythagorean Theorem giving examples from two of your summer jobs Did not identify when to use the Pythagorean Theorem OR give examples from two of your summer jobs Identify when to use the Pythagorean Theorem without giving examples from two of your summer jobs Identify when to use the Pythagorean Theorem giving examples from one of your summer jobs Identify when to use the Pythagorean Theorem giving examples from two of your summer jobs Apply the Pythagorean Theorem: Give the solutions to job related tasks from two of your summer jobs Did not apply the Pythagorean Theorem by giving the solutions to job related tasks from two of your summer jobs --- Apply the Pythagorean Theorem: Give the solutions to job related tasks from one of your summer jobs Apply the Pythagorean Theorem: Give the solutions to job related tasks from two of your summer jobs Explain the Trig Ratio (Sine) using the formula and a sketch No explanation, formula or sketch of the Trig Ratio (Sine) Errors in explanation of the Trig Ratio (Sine) OR missing the formula and a sketch Some errors in explanation of the Trig Ratio (Sine) OR missing the formula or a sketch Accurate explanation of the Trig Ratio (Sine) using the formula and a sketch Identify when to use the Trig Ratio (Sine) giving examples from two of your summer jobs Did not identify when to use the Trig Ratio (Sine) OR give examples from two of your summer jobs Identify when to use the Trig Ratio (Sine) without giving examples from two of your summer jobs Identify when to use the Trig Ratio (Sine) giving examples from one of your summer jobs Identify when to use the Trig Ratio (Sine) giving examples from two of your summer jobs Apply the Trig Ratio (Sine): Give the solutions to job related tasks from two of your summer jobs Did not apply the Trig Ratio (Sine): by giving the solutions to job related tasks from two of your summer jobs --- Apply the Trig Ratio (Sine): Give the solutions to job related tasks from one of your summer jobs Apply the Trig Ratio (Sine): Give the solutions to job related tasks from two of your summer jobs Explain the Trig Ratio (Cosine) using the formula and a sketch No explanation, formula or sketch of the Trig Ratio (Cosine) Errors in explanation of the Trig Ratio (Cosine) OR missing the formula and a sketch Some errors in explanation of the Trig Ratio (Cosine) OR missing the formula or a sketch Accurate explanation of the Trig Ratio (Cosine) using the formula and a sketch Identify when to use the Trig Ratio (Cosine) giving examples from two of your summer jobs Did not identify when to use the Trig Ratio (Cosine) OR give examples from two of your summer jobs Identify when to use the Trig Ratio (Cosine) without giving examples from two of your summer jobs Identify when to use the Trig Ratio (Cosine) giving examples from one of your summer jobs Identify when to use the Trig Ratio (Cosine) giving examples from two of your summer jobs Apply the Trig Ratio (Cosine): Give the solutions to job related tasks from two of your summer jobs Did not apply the Trig Ratio (Cosine): by giving the solutions to job related tasks from two of your summer jobs --- Apply the Trig Ratio (Cosine): Give the solutions to job related tasks from one of your summer jobs Apply the Trig Ratio (Cosine): Give the solutions to job related tasks from two of your summer jobs Explain the Trig Ratio (Tangent) using the formula and a sketch No explanation, formula or sketch of the Trig Ratio (Tangent) Errors in explanation of the Trig Ratio (Tangent) OR missing the formula and a sketch Some errors in explanation of the Trig Ratio (Tangent) OR missing the formula or a sketch Accurate explanation of the Trig Ratio (Tangent) using the formula and a sketch Identify when to use the Trig Ratio (Tangent) giving examples from two of your summer jobs Did not identify when to use the Trig Ratio (Tangent) OR give examples from two of your summer jobs Identify when to use the Trig Ratio (Tangent) without giving examples from two of your summer jobs Identify when to use the Trig Ratio (Tangent) giving examples from one of your summer jobs Identify when to use the Trig Ratio (Tangent) giving examples from two of your summer jobs Apply the Trig Ratio (Tangent): Give the solutions to job related tasks from two of your summer jobs Did not apply the Trig Ratio (Tangent): by giving the solutions to job related tasks from two of your summer jobs --- Apply the Trig Ratio (Tangent): Give the solutions to job related tasks from one of your summer jobs Apply the Trig Ratio (Tangent): Give the solutions to job related tasks from two of your summer jobs PowerPoint Score Total Score

back to top Conclusion

You are now familiar with the trigonometry ratios as well as the Pythagorean theorem. You have also seen how these ideas are used in the real world. What you have done here is just the beginning of how the measurement of triangles plays an important role in the world in which we live. How else might you see trigonometry as being useful to you in the future? What if you were a sailor and had to know how far away the lighthouse is so you don't crash into the rocks? What if you were scuba diving and needed to know how much father your air hose would go? What are other areas of work you might do that could require you to know how to figure out lengths and angles of triangles or other polygons? Credits & References

Special thanks to Ms. Amyot, Mrs. Conti and Mr. Hebrank for all of your math help!

Cooper, M. (2005, November 22) Conviction With an Angle Is Upheld by Court of Appeals. The New York Times. Retrieved April 13, 2008, from: http://www.nytimes.com/2005/11/23/nyregion/23drugs.html

Definition of Pythagoras Theorem. (2007, November 26). Retrieved April 13, 2008 from Math is Fun: http://www.mathsisfun.com/definitions/pythagoras-theorem.html

Drexel University. (1996, August 20) Ask Dr. Math: What is Trigonometry. Retrieved April 13, 2008 from Math Forum: http://mathforum.org/library/drmath/view/54003.html

Eisenberg, J. D. (2006). Trigonometry - Surveying Uses. Retrieved April 17, 2008 from Cat Code: http://catcode.com/trig/trig13.html

Geometry and Trigonometry Reference Area. (c2007) Retrieved April 13, 2008 from Cool Math: http://www.coolmath.com/reference/geometry-trigonometry-reference.html

Maths First. (2006, August 9). Trigonometry Index, Maths First, Institute of Fundamental Sciences, Massey University. Retrieved April 13, 2008, from Massey University: http://mathsfirst.massey.ac.nz/Trig.htm

Oswego City School District. (c2008) Pythagorean Theorem. Retrieved April 17, 2008 from Regents Prep: http://www.regentsprep.org/Regents/math/ALGEBRA/AT1/Pythag.htm

Oswego City School District. (c2008) Right Triangle Trigonometry: Solving for a side. Retrieved April 17, 2008 from Regents Prep: http://www.regentsprep.org/Regents/math/ALGEBRA/AT2/Ltrig.htm

Oswego City School District. (c2008) Right Triangle Trigonometry: Solving for an angle. Retrieved April 17, 2008 from Regents Prep: http://www.regentsprep.org/Regents/math/ALGEBRA/AT2/LtrigA.htm

Spector, L. (c2008) Three-place Trigonometry Table. Retrieved April 20, 2008 from The Math Page: http://www.themathpage.com/aTrig/trigonometric-table.htm

Fishing image from Math Supporter

More Trigonometry Links

Trigonometry Review. (c2006) Retrieved April 13, 2008 from Curriculum Bits: http://www.curriculumbits.com/prodimages/details/maths/mat0003.html

University of Regina. What are Real World Applications of Trigonometry. Retrieved April 13, 2008 from Math Central: http://mathcentral.uregina.ca/RR/database/RR.09.01/trigexamples1.html

Utah State University. (c2007) Pythagorean Theorem. Retrieved April 13, 2008 from National Library of Virtual Manipulative: http://mathcentral.uregina.ca/QQ/database/QQ.09.07/h/albetel1.html Last updated on April 27, 2008. Based on a template from The WebQuest Page