Just how accurate is right triangle trigonometry?
ProcessBefore you begin, you should be aware that this WebQuest is divided into two pieces, based on which questions you are working on.
- Questions 1-6 require you to solve problems and explain your solutions. - Questions 7-10 require you to reflect on your answers from 1-6. If at any time you are confused by the directions or by a problem, please raise your hand and your teacher will be over to help you. Directions: For questions 1-6, answer the question using what you know about right triangle trigonometry. Also, explain why you did what you did to find the solution. The * symbol is used to represent "degrees". Use complete sentences, and show all your work. NOTE: "Why" means why you knew to use the quadratic formula, not what you did with the quadratic formula. 1) You are standing a little less than 100 feet from the Eiffel Tower in Paris, France. You look up to the top of the tower at what you estimate is about a 85* angle. Find the height of the Eiffel tower. Describe the process you used, and why you knew to do each step 2) From the top of the Grand Canyon, you can see that the deepest part is about 1500 feet in from the edge where you stand. If you look down at 75*, what is the deepest point in the Grand Canyon? Describe the process you used, and why you knew to do each step. 3) From the side of the Golden Gate Bridge in San Francisco, you can see the markings on the pillars that display the water depth. After some calculations, you find that the bridge stands about 200 feet above the water at the center of the bridge. The angle that you look down toward the water on is about 25*. How far away from the center of the bridge are you standing? Describe the process you used, and why you knew to do each step. 4) While visiting Seattle, you decide to see the Space Needle. You estimate that you are standing almost 500 feet away. From this point, you look up at the top and see that it is about a 50* angle. Based on this information, how tall is the Space Needle? Describe the process you used, and why you knew to do each step. 5) In Bangladesh, India, the first man to attempt to find the size of Mt. Everest used Trigonometry. Knowing this, you decide to calculate how tall the mountain is in the same way. You know that you are about 5 miles away from the peak. From here, you look up at about 45* to the top of the mountain. Find the height of Mt. Everest. (1 mile = 5280 feet) Describe the process you used, and why you knew to do each step. 6) On a sight-seeing cruise, you spot some Orca whales in a dive. You figure that the whales are only about 80 feet from the surface of the water. You are looking down on the whales at about a 60* angle. The cruise director wants to move so the ship is directly above the whales at their current location. Find how far the ship needs to move. Describe the process you used, and why you knew to do each step. Directions: Use your answers for questions 1-6 to assist you in answering the following questions. You may be required to research different information before you can appropriately answer the questions below. Be prepared to jot down important information as you complete this research. Write your answers to questions 7-10 in the same place that you wrote your answers to questions 1-6. All answers should be written in complete sentences.
7) Using the links below, see how close your answers from questions 1-6 are to the actual answers. For questions where you solved for how far away you are standing from a structure or object, check to see if the actual height you used in the problem matches with the actual height you find in your research. Be sure to answer these 2 questions for EACH of the problems you solved previously: 1. How accurate are your answers? 2. Are you within 1 unit? 10 units? 100 units? Eiffel Tower Problem http://www.tour-eiffel.fr/teiffel/uk/ http://en.wikipedia.org/wiki/Main_Page http://www.endex.com/gf/buildings/eiffel/eiffel.html Grand Canyon Problem http://en.wikipedia.org/wiki/Main_Page http://www.nps.gov/grca/index.htm http://www.grand.canyon.national-park.com/ Golden Gate Bridge Problem http://en.wikipedia.org/wiki/Main_Page http://goldengatebridge.org/ http://www.sfmuseum.org/hist9/mcgloin.html Space Needle Problem http://en.wikipedia.org/wiki/Main_Page http://www.historylink.org/_output.CFM?file_ID=1424 http://www.emporis.com/en/wm/bu/?id=119476 Mt. Everest Problem http://en.wikipedia.org/wiki/Main_Page http://www.mnteverest.net/history.html http://www.peakware.com/index.html Orca Problem http://www.antarcticconnection.com/antarctic/wildlife/whales/orca.shtml http://www.enchantedlearning.com/subjects/whales/species/Orca.shtml 8)Research what “accuracy” means using the links below. How can you explain the amount of accuracy in your answers? http://www.flatsurv.com/accuprec.htm http://en.wikipedia.org/wiki/Main_Page 9) What could you do to make your answers for 1-6 more accurate? How could you make your answers less accurate? 10) Under what circumstances would you need to be more accurate? Give at least 2 different examples of when accuracy is necessary. When you have completed all of the problems from 1-10, ask your teacher what you need to turn in to get your project grade. After you have spoken with your teacher, you may click on the link that says "Conclusion". |