Trigonometric Functions WebQuest

Introduction:

By Christopher Caschera, Geometry Period 1

 This investigation is about Trigonometric ratios and functions, in this lesson you will develop a deep understanding of this concept and will grasp key ideas like tangent, cosine, and sine very well. Throughout the investigation, you will be able to see what real life builders of many cities see when they look at building another skyscraper next to the other. You will also see why the builders also take into account the shadow their new buildings will cast and you will figure out their problems with some really cool real life scenarios!

Let’s have fun!!! :)

Who’s ready to build?

After your completion of this WebQuest, you will be able to understand the key features associated with Trigonometric ratios and functions, and be able to use them in real life scenarios and solve them.

 

Task 1: Familiarize yourself with Trigonometry concepts such as the Pythagorean Theorem, trig ratios and such to accomplish these real life tasks.

 

Task 2: Read the scenarios as you now possess the knowledge to solve these everyday problems a construction worker/engineer faces.

 

Task 3: With your new acquired data, make a Powerpoint with the included data and your solved problems.

Task 1:

Read all of the following links and acquire more information on the subject! Take notes on the Pythagorean Theorem, Trig Ratios, Trigonometric functions, and anything else you might find useful and helpful. After done with researching, you should be able to have a better understanding of what you’re expected to know as an engineer in real life scenarios.

 Websites to take notes on:

http://www.mathsisfun.com/pythagoras.html  (Pythagorean Theorem)

 

http://www.purplemath.com/modules/basirati.htm (Trig Ratios)

 

http://www.mathsisfun.com/algebra/trigonometry.html (Trigonometry)

 

 Note: Please remember your notes will be useful later.

 P.S.  It also might help to remember these specific functions for Trigonometric ratios in the song (SOH, CAH, TOA) where “o” is the opposite, “a” is the adjacent, and “h” is the hypotenuse. And you need a Scientific Calculator.

 

Task 2:

 Knowing that you have an outstanding record and resume, your new boss for “We Build Skyscrapers” as hired you as the new head engineer on a few projects going on in New York City’s financial district. Before you go on your way, he gives you a file of each building’s location and current scenario. Your job is clear: to do as he says in the documents and get the job done the right way.

Job #1 “Penn State Building”

 Note: Round to the nearest tenth for all the jobs.

The land around the soon to be “Penn State Building” is being cleared in the shape of a right triangle. Since both posts for the building are already in the ground, you can assume a wall has already been built as well between them. The distance they’re from each other represent 100 ft. The angle that the shadow of the two structures casts on the ground makes is 35 degrees. The Hypotenuse c is yet to be figured out in the nearest tenth of a foot. Here is a basic model of what you will be working with:

 

Job #2 “The Twin Towers”

Note: Towers are not the exact same.

Your boss has authorized you clearance on participating in the building of the new Twin Towers.  The mayor of NYC specifically wanted right triangle shaped buildings because the NYC skyline lacks them. But, it has recently come to his attention that something is wrong with the design of both of the towers itself. Your job here is to figure out what angle the shadow (rounded to the nearest whole number/angle) of the second tower when given that the sadow’s length equals c=620 ft,. and leg a=200 ft. and the first tower with the longest side being 1,260 ft. and an angle of 80 to solve for the shortest leg. Here is the model of the buildings your boss gave you:

Job #3 “Fast Food City”

 A new company is interested in moving in the city’s “Triangle District”. Though this is a good thing, there’s one problem: space. Since this is a difficult job, your boss thinks it’s time to finally prove yourself by showing him you can complete something many have trouble with. Now that you know space is an issue, your boss wants you to create ratios that can be used to see if your trigonometry team can come in later and see what they can do. The following model is what building you have to work with and the point of the building you have to find is A:

 

Task 3:

The boss has asked you to make a PowerPoint presentation to present to your newer coworkers tomorrow morning. He has required you to put all your data inside from today’s work, and your WORK MUST BE SHOWN   in order for the boss to see that you truly have what it takes to exist in this company for years to come!

Category:	4 Meets Requiremts & more	3 Meet Requirements	2 Barely Meets Requirements	1 Does not meet expectation
Mathematical Concepts	The concepts are well used throughout their notes and can accurately propose answers to the problems.	Has an accurate understanding of MOST topics.	Has some experience with topic and can somewhat answer the questions.	No prior knowledge and can be found because of invalid answers.
Creativity	Powerpoint and explanations are well presented in a digital version and written.	There is a mostly accurate amount of responses present in the Powerpoint.	Presentation and project is somewhat correct but still way off in terms of explanations.	Creative output is low to none.
Explanations	Are well created and explained to best of ability.	There’re well created explanations with mostly correct statements.	Some correct explanations with correct answers.	No correct explanations present or not found.
Task Completeness	Completes all task in a reasonable amount of time and more	Tasks are complete, but lack in work/answers	Some tasks are complete or solved to best of ability	Problems are either not solved completely or not at all
Internet use	Uses all of suggested websites and takes note of important facts present in presentation	Websites are used, but project is lacking in excess of creative topics	Some websites are used and some information from them is present in their work	Does not use the suggested websites at all or not enough information is known
Score:

Right Triangle Similarity can be used in many fundamental ways in real-life. The knowledge that you have now gained from this WebQuest and the associated problems will serve to help you in the near future and whatever endeavors you do. Your knowledge of Trig and ratios should take you far in your life now. Even though it seems like you will never use this, remember that math is everywhere and you will always use something again in your life at some time. My hope is that the lesson present in the WebQuest has helped you a lot.

 

My name is Christopher Caschera and I am a currently at the end of my Geometry class. I have much experience with Geometry now because of my studies, and I want to help you succeed as well. I am a very good person in real life, and always try to help people with math or whatever’s needed. I wrote this WebQuest to better your understanding on an important topic for the EOC/End of Course Exam. I also want to see you succeed in real life scenarios like this or in your studies. Thank you, and I hope this WebQuest helps you a lot.