mrs. badr's class · web viewnoah howard 2. jacob corpus 3. lindsey graca 4. gabby swenson 7....

Unit 2: Law of Sines and Law of Cosines Applications (updated 10/28)

Monday

10/24

Bearings Lesson

Bearings Worksheet

Tuesday

10/25

Finish Bearings Worksheet

(due end of hour)

Wednesday

10/26

Lesson: Examples of Law of Sines and Law of Cosines Applications

Thursday

10/27

Work on Practice 1-3

Friday

10/28

(1/2 day)


Finish practice 1 due Monday at the beginning of class.

Monday

10/31

Halloween Activity

Practice 1 Due by start of class.

Finish practice 2 due Tuesday at the beginning of class.

Tuesday

11/1


Finish practice 3 due Wednesday at the beginning of class.

Wednesday

11/2

Work on Practice 3 and the Review


Thursday

11/3

Work on the Review/Q & A


Finish review sheet, it is due at the beginning of class on Friday

Friday

11/4

Unit 2 Applications Test (100 points)

Review Sheet due at the beginning of class.

Groups and Location Assigned

3rd Hour Groups

1. Southeast Asia

1. Ava Temple

2. Sophia Sarti

3. Brittany Leist

2. South America

1. Jayson Long

2. Josh Zurek

3. Brian Crawford

3. Caribbean and the Bahamas

1. Autumn Fuchs

2. Bella Smith

3. Megan Horak

4. Kylie Forrrest

4. Mexico and Central America

1. Sierra Bayha

2. Baylee Edwards

3. Kate Winter

4. Emily Blanzy

5. Europe and the Mediterranean

1. Alexis V.

2. Amanda Gore

3. Julia Janowiak

4. Rachel Phillips

6. Asia, Africa and the middle east

1. Joel Woody

2. Michael Jacobs

3. Dominic Warner

4. Tripp Trevision

7. Hawaii

1. Stephanie Wright

2. Lindy White

3. Cameron Schimp

8. Alaska

1. Julian Alvarado

2. Brenden Davidson

3. Hunter Overall

4. Corby Cronk

5th Hour Groups

1. Southeast Asia

1. Chris Alvira

2. Drew Wickland

3. Chase Respond

4. Peter Hogan

2. South America

1. Maria Fekaris

2. Brianna Watkins

3. Jordyn Bard

4. Julie Crawford


1. Dawson Zabawa

2. Nick Bourns

3. Caelen Pavlak

4. Brianne Janssen


1. Hunter Nigg

2. Trent Confer

3. Samantha V.

4. Anna Thompson


1. Michell Boles

2. Alec Ramirez

3. Hannah Folkmier

4. Abigail Wozny


1. Sam Beagan

2. Mckenna Kiel

3. Tyler Daily

6th Hour Groups

1. Southeast Asia

1. Jessica Stuart

2. Avery Tardiff

3. Mackenzie Ludwig

4. Lucy George

2. South America

1. Hanna Ballard

2. Brian Clink

3. Addison Johnson

4. Dylan McKinzie


1. Sophia Zalupski

2. Bianca Zaguroli

3. Allan Stone

4. Zach Falzon


1. Justin Kleckner

2. John Horten

3. Elizabeth Hunt

4. Julia Kulesza


1. Nick Lieske

2. Claire Brewer

3. Gabriella Kasabasic


1. Noah Howard

2. Jacob Corpus

3. Lindsey Graca

4. Gabby Swenson

7. Hawaii

1. Alana Paterra

2. Grace Maxwell

3. Phillip Layman

4. Nick Mcc.

8. Alaska

1. Femi Kuforgi

2. Matthew Bycraft

3. Brenden O’Dell

Bearings Worksheet

Name: ________________________________Hour:______

1. The bearing of a buoy from a ship 8.7 miles away is N64°E. The ship is headed du north, and the navigator plans to change course when the buoy has bearing of S26°E. How much farther will the ship travel before a change of course is needed?

2. A pilot of a San Antonio-to-Houston express plane traveling on a course of N79°E sights the Austin Airport off the left side of the plane. His line of sight forms a right angle with the plane’s line of travel. Find the bearing of the Austin Airport from the airplane.

3. After the plane in problem #2 travels 45 minutes (from the first sighting of the airport) at 180 mi/hr along the same course, the airport has a new bearing of N80°W. How far is the plane from the airport?

4. The navigator of a ship on a N44°E course sights a buoy with a bearing of S46°E After the ship sails 15 km along the same course, the navigator sights the same buoy a bearing S 12°F. Find the distance between the ship and the buoy at the time of each sighting.

5. The angle of depression from a helicopter to its landing port is 64°. If the altitude the helicopter is 1600 meters, find the direct distance from the helicopter to the landing port.

Answers

1. l985 miles

2. N11°W

3. 144.6 miles

4. 1t sighting: 22.2 km

2 sighting: 26.8 km

5. 1780.16 meters

Applications of the Law of SinesName: ___________________________ Hour: _______

1.

2.

3.

Answers: 1) 15.3 meters, 2) 77 meters, 3) 3.2 miles

Applications of the Law of Cosines Name: ________________________ Hour: _____

1.

2.

3.

Answers: 1) 373.3 meters, 2) N 58.4°W, 3) 24.2 miles

Name: ______________________________ Hour: _______

Mixed Law of Sines/Law of Cosines Applications (no bearings problems) --- Practice 1

1. Two ranger stations located 10 km apart on the southwest and southeast corners of a national park. They receive a distress call from a camper. Electronic equipment allows SW ranger to determine that the camper is at a location that makes an angle of 61 with the southern boundary. Another beacon allows the SE ranger see that the camper is 9.2 km to the northwest of his position. (a) Which station is closer to the camper? (b) What is the difference in the distances?

2. Ships A and B leave port at the same time and sail on straight paths making an angle of 60 with each other. How far apart are the ships at the end of 1 hour if the speed of ship A is 25km/h and that of ship B is 15 km/h?

3. A plane flies 500 miles on a straight path. The plane then turns left 12 degrees on a new heading and goes another 300 miles. How far is the plane from its original location?

4. A boat leaves a pier heading due north for 50 miles. The captain then turns 20° toward the west and goes another 10 miles. At this point the boat breaks down. What angle (from north) does the harbor need to send a tug boat to retrieve the boat and the captain?

5. The angles of elevation of a balloon from the two points A and B on level ground are 24 and 47 respectively. If points A and B are 8.4 miles apart and the balloon is between the points, in the same vertical plane, approximate, to the nearest tenth of a mile, the height of the balloon above the ground.

6. After a storm, a tree is leaning 3° from vertical toward the front of a house. A person standing on the front porch notices that the angle of elevation to the top of the tree is 40°. If the house is 60 feet from the base of the tree, how tall is the tree?

7. A ship in the bay is 18 miles from one lighthouse and 30 miles from another. What is the distance between lighthouses if the measure of the angle formed by the line of sight to the lighthouse is 130?

8. A vertical flagpole is mounted on a hill that makes a 10o angle with the horizontal. If the sun, shining at an angle of elevation of 70o, makes a 13 foot shadow down the hill, how tall is the flagpole?

9. A tree is leaning 5° from vertical up a hill that makes an angle of 15o with the horizontal. The sun, shining at an angle of elevation of 60o, makes a shadow up the hill. If the tree is 45 feet tall, how long is the shadow?

Key:

1. (A) the SW station is closer (b) 9.2-7.7 = 1.5 km apart

2. 21.8 km

3. 795.8 mi

4. 3.3°

5. 2.6 mi

6. 48.3 ft.

7. 43.8 mi

8. 32.9 ft.

9. 26.7 ft.

Name: ______________________________ Hour: _______

Law of Sines Applications (includes bearings)—Practice 2

1. The distance between Towns A and B is 56 mi. The angle formed by the road between Towns A and B and the road between Towns A and C measures 46. The angle formed by AB and BC measures 115. Find the distance between Town B and Town C.

2. On a ship sailing north, a woman notices that a hotel on a shore has a bearing of N 20⁰ E. A little while later, after having sailed 40 km, she observes that the bearing of the hotel is now S 80⁰ E. How far is the ship from the hotel?

3. A ship is steaming south. The navigator notices that the bearing of a lighthouse is S 30⁰ W. After moving 8.0mi/h for 2 h, he observes that the bearing of the lighthouse is N 25⁰W. Find his distance from the lighthouse at the time of the second sighting.

4. Bill determines that the angle of elevation to the top of a building measures 40.5°. If he walks 102 ft. closer to the building, the measure of the new angle of elevation will be 50.3°. Find the height of the building.

5. John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33º. This particular tree grows at an angle of 83º with respect to the ground rather than vertically (90º). How tall is the tree?

6. A building is of unknown height. At a distance of 100 feet away from the building, an observer notices that the angle of elevation to the top of the building is 41º and that the angle of elevation to a poster on the side of the building is 21º. How far is the poster from the roof of the building?

7. An observer is near a river and wants to calculate the distance across the river. He measures the angle between his observations of two points on the shore, one on his side and one on the other side, to be 28º. The distance between him and the point on his side of the river can be measured and is 300 feet. The angle formed by him, the point on his side of the river, and the point directly on the opposite side of the river is 128º. What is the distance across the river?

Key

1. The distance between Town B and Town C is 123.731 miles.

2. The ship is 13.892 km from the hotel.

3. The ship is 9.766 miles from the lighthouse at the second sighting.

4. The building is 298.581 ft. tall.

5. The tree is 74.470 feet tall if it is leaning away from John. The tree is 59.167 feet tall if it is leaning toward John.

6. The poster is 48.543 feet from the roof of the building.

7. The distance across the river is 34.627 ft.

Name: ______________________________ Hour: _______

Mixed Law of Sines/Law of Cosines Applications (includes bearings) --- Practice 3

1. Juan and Romella are standing at the seashore 10 miles apart. The coastline is a straight line between them. Both can see the same ship in the water. The angle between the coastline and the line between the ship and Juan is 35 degrees. The angle between the coastline and the line between the ship and Romella is 45 degrees. How far is the ship from Juan?

2. Jack is on one side of a 200-foot-wide canyon and Jill is on the other. Jack and Jill can both see the trail guide at an angle of depression of 60 degrees. How far are they from the trail guide?

3. Tom, Dick, and Harry are camping in their tents. If the distance between Tom and Dick is 153 feet, the distance between Tom and Harry is 201 feet, and the distance between Dick and Harry is 175 feet, what is the angle between Dick, Harry, and Tom?

4. Three boats are at sea: Jenny one (J1), Jenny two (J2), and Jenny three (J3). The crew of J1 can see both J2 and J3. The angle between the line of sight to J2 and the line of sight to J3 is 45 degrees. If the distance between J1 and J2 is 2 miles and the distance between J1 and J3 is 4 miles, what is the distance between J2 and J3?

5. Airplane A is flying directly toward the airport which is 20 miles away. The pilot notices airplane B 45 degrees to her right. Airplane B is also flying directly toward the airport. The pilot of airplane B calculates that airplane A is 50 degrees to his left. Based on that information, how far is airplane B from the airport?

6. A plane leaves JFK International Airport and travels due west at 570 mi/hr. Another plane leaves 20 minutes later and travels 22º west of north at the rate of 585 mi/h. To the nearest ten miles, how far apart are they 40 minutes after the second plane leaves.

7. Flights 104 and 217 are both approaching O’Hare International Airport from directions directly opposite one another and at an altitude of 2.5 miles. The pilot on flight 104 reports an angle of depression of 17.6º to the tower, and the pilot on flight 217 reports an angle of depression of 12.4º to the tower. Calculate the distance between the planes.

8. A triangular playground has sides of lengths 475 feet, 595 feet, and 401 feet. What are the measures of the angles between the sides, to the nearest tenth of a degree?

1. 7.2 miles

2. 200 feet

3. 47°

4. 2.94 miles

5. 18.5 miles

6. 430.7 miles

7. 19.25 miles

8. 52.7°, 42.2°, 85.1°

mrs. badr's class · web viewnoah howard 2. jacob corpus 3. lindsey graca 4. gabby swenson 7....

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