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Chapter 4, Section 4-8, Solving Problems with Trigonometry HW: pg 393 – 398: #’s 9, 10, 14-17, 25, 26 I. Using Inverse Trigonometric Functions Georgia Power installed a nest camera in a pine tree to enable bird watchers to view a male and female bald eagle pair (bald eagles mate for life) and their offspring on the campus of Berry College in Rome, Georgia. http://www.berry.edu/eaglecam/ http://www.wsbtv.com/videos/news/watch-bald-eagle-fends-off-attack-by-owl-onberry/vCRW75/ Photo links: http://search.tb.ask.com/search/AJimage.jhtml?&searchfor=berry+college+eagle+cam+photos+2015&ts= 1424183520941&p2=%5EBE4%5Exdm111%5ETTAB01%5Eus&n=780cbc7d&ss=sub&st=tab&ptb=32AA54D F-ABEA-487D-A569-BD8420914EEC&si=dmgrplus&tpr=sbt&imgsize=all&safeSearch=on&imgDetail=true Example A: Suppose the eagles’ nest is 100 feet up in the pine, and Berry College Eagle Expert and Biology Professor Renee Carleton has set up a camouflaged observation blind on the ground 200 feet away. What is the angle of elevation of the blind to the eagle’s nest in the tree? Round your answer to the nearest degree and minute. First, draw a sketch to represent the problem. Review: 1° = 60 minutes or 60′. II. Making Indirect Measurements Example A (teacher guided): You are a spectator at the Lumberjack World Championships in Hayward, Wisconsin, and the 90-foot men’s pole climb competition is about to begin. A support cable for a cedar pole makes an angle of depression that is 78 degrees. From your seat in the bleachers, your line of sight to the top of the pole forms an angle of elevation that is 32 degrees. If your line of sight is 10 feet up in the air, how far away from the support cable and the pole are you? Round your answers to the nearest foot. Draw a sketch to represent the problem. After we solve the problem, we will watch the youtube video linked below. Photo Source: http://en.wikipedia.org/wiki/File:SpeedClimb.jpg http://www.youtube.com/watch?v=rFVqMO48RWQ Example B: Student independent work Source: http://en.wikipedia.org/wiki/File:North_face.jpg The Eiger’s North Face in the Swiss Alps rises about 3000 meters above the village of Grindlwald From the terrace of the Bodenwald Chalet in Grindlwald, the angle of elevation to the summit of the Eiger’s North Face is 50 degrees. You decide to save some money on accommodations, and your campsite is a bit further and forms an angle of elevation of 43 degrees to the North Face peak. After a long day of hiking, how far do you have to walk from your campsite to the Bodenwald Chalet terrace where you will eat some hearty food and listen to traditional music? In the space above, draw a sketch to represent the problem and then solve the problem, showing work below and rounding your answer to the nearest meter. After solving the problem, we will click on the link below to listen to a clip from the newest CD of the Jossi-Buebe. http://bodenwald.ch/index.php?userlang=en&page=restaurant III. Finding Height Above Ground Sixteen huge helium-filled balloons floated in the 87th Annual Macy’s Thanksgiving Day Parade in New York City on November 28, 2013. Due to windy conditions, New York Police asked that the balloons be flown at half their normal height. In addition, a police sergeant walked along with each of the sixteen big balloons for safety reasons. Example A: Rows of parade volunteers pull a huge, helium-filled Sponge Bob Square Pants balloon around Central Park using guide wires. The angle of depression of the first set of guide wires from the base of Sponge Bob Square Pants to the handlers’ hands, about four feet in the air, is 71 degrees. From a similar height of four feet, a policeman creates an angle of elevation of 50 degrees. If the policeman is 5 feet in front of the first row of handlers, how high are the balloons flying? To get a sense of this problem, click on the following link to a photo series of the November, 2014 parade: http://www.nytimes.com/2014/11/28/nyregion/macys-thanksgiving-parade-new-york-fergusonprotesters.html?action=click&pgtype=Homepage&version=Moth-Visible&module=inside-nytregion®ion=inside-nyt-region&WT.nav=inside-nyt-region First, draw a sketch to represent the problem, and then solve the problem. Example B: Ecuador Cloud Forest Mrs. Ector and her Precalculus class embark on an eco-trip to the *cloud forest in Mindo, Ecuador. They stay in the Yellow House Eco Lodge and go bird watching and orchid photographing. In addition, they take a day hike up the Pichincha Volcano with a local guide. Source: http://www.merriam-webster.com/dictionary definition of a cloud forest: a wet tropical mountain forest at an altitude usually between 3000 and 8000 feet (1000 and 2500 meters) that is characterized by a profusion of epiphytes and the presence of clouds even in the dry season Source: https://www.rainforestrescue.org.au/page/87/ecuador-cloud-forest-biodiversity “…the Ecuador Cloud Forests are considered the single richest hotspot on the planet, containing approximately 15-17% of the world’s plant species and nearly 20 of its bird diversity.” Source: http://en.wikipedia.org/wiki/File:Rucu_Pichincha_and_Trail.jpg The initial embarkation point at the base of Pichincha forms an angle of elevation of 40 degrees and 20 minutes. The students and Mrs. Ector walk 120.3 meters towards the mountain, and the angle of elevation becomes 44 degrees and 24 minutes. What is the elevation of Pichincha’s highest peak, the Guagua, considering that the elevation above sea level is 4000 meters at the base? https://www.rainforest-rescue.org/mailalert/962/ecuador-trashing-a-cloud-forestfor-copper Ecuador: trashing a cloud forest for copper? Codelco, a company owned by the Chilean state, wants to mine for copper in Ecuador’s rainforest – bad news for nature, biodiversity and water resources. We can’t let this happen. Please lend your voice to our petition. Label the angles of elevation on the diagram below and also add the distance of 120.3 meters. Then show work for solving the problem using trigonometric ratios. Pichincha’s highest peak, the Guagua, has an elevation of ________________meters above sea level. A photo of the 1999 blast of the volcano which deposited 3 inches of ash on the surrounding area. Source: http://en.wikipedia.org/wiki/File:Erupcion_guagua_rgb.jpg Yellow House Eco Lodge: http://ecuadormindobirds.com/index.html Orchids: http://www.bellavistacloudforest.com/#/orchids/4574007611 Birds: http://www.bellavistacloudforest.com/#/birding/4574002804 IV. Trigonometry in Navigation Recall that course bearings are three digit numbers and the course of a plane or ship is measured clockwise from the North. A. B. C. A shows a course bearing of 110°; B shows a course bearing of 240°; C shows a course heading of 050°. Bearing example: Two radar towers 5 miles apart are tracking a UFO. Tower A tracks the UFO at a bearing of 50° and tower B tracks it at 320°. The triangle formed between the two towers and the UFO is a right triangle. How far is the UFO from the radar towers? Draw a sketch to represent the problem. Round your answers to the nearest tenth of a mile.