Download Chapter 4, Section 4-8, Solving Problems with Trigonometry File

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&region=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.