Pre-Calculus Unit 4- 1st 9-weeks



Pre-Calc Unit 6 2nd Term Nov. 8th to Nov. 17th 2011

6.1 Law of Sines and 6.2 Law of Cosines

|Date |Topic |Assignment |Did IT |

|Tuesday |6.1 6.1 Law of Sines, Area of an Oblique Triangle |Book: p. 436 #s 1-8, 29, 30 | |

|11/8 | | | |

|Wednesday |6.2 Law of Cosines, Heron’s Area Formula |Book: p. 443 #s 1-10, 23-26 | |

|11/9 | | | |

|Thursday |6.1, 6.2 Application Problems notes pp 1- 2 |Worksheet pp 2-4 | |

|11/10 | | | |

|Friday |6.1, 6.2 Application Problems con’t. |Worksheet pp 4-5 | |

|11/11 |Quiz: Law of Sines, Law of Cosines, Area of a Triangle | | |

|Monday |6.1, 6.2 Application Problems con’t |Book: p. 444 #s 31-35, 39-42 | |

|11/14 | | | |

|Tuesday |District Assessment |Book: pp. 482-483 #s 1, 3, 13, | |

|11/15 | |23, 33 | |

|Wednesday |Review Quiz : application Problems |Study for test | |

|11/16 | | | |

|Thursday |Test #6 |Print out Unit 7 | |

|11/17 | | | |

Notes Thursday 11/10 For each of the following: 1. Draw a triangle. 2. Solve. Show all work

Angle of elevation: represents the angle from the horizontal upward to an object.

Angle of depression: represents the angle from the horizontal downward to an object.

1. Two planes leave an airport at the same time. Plane A travels at 500 mph, while Plane B travels at 350 mph. How far apart will they be after 3 hours if the angle between their paths is 56[pic]?

2. While on a family vacation in Egypt, you are standing outside one of its great pyramids. Bored of the tour, you decide to take on some “practical” applications of your Pre-Calculus class. With a meter stick (that you always carry with you just in case), you measure the base of the pyramid to be 230 m. With your protractor, you find that the faces of the pyramid make an angle of 51.2[pic] with the ground. How tall is the pyramid?

3. You are asked to find the height of a nearby building. From where you initially stand, you measure the angle of elevation to be 36[pic]. Moving closer to the building by 50 feet, the angle of elevation becomes 58[pic]. To the nearest foot, what is the height of the building?

p 1

4. The ramp leading to a bridge must gain 8 feet in elevation. If the angle of elevation of the ramp is to be 4[pic], find the length of the ramp.

5. Luke Skywalker must visit three planets (Yavin, Endor, and Hoth). Yavin and Endor are 34 parsecs apart, Endor and Hoth are 53 parsecs apart, while Hoth and Yavin are 70 parsecs apart. What is the measure of the largest angle between all the planets?

6. A surveyor is standing 115 feet from the base of the Washington Monument. The surveyor measures the angle of elevation to the top of the monument as 78.3˚. How tall is the Washington Monument?

7. A historic lighthouse is 200 yards from a bike path along the edge of a lake. A walkway to the lighthouse is 400 yards long. Find the acute angle θ between the bike path and the walkway.

8. Find the length of a skateboard ramp when the height of the ramp is 4 feet and the angle formed where the ramp touches the ground is 18.4˚.

Homework 11/10 Draw a Picture. Solve using the Law of Sines, Law of Cosines, or Right Triangle Trig. Round to two decimal places. Show all work

1. Bilbo and Frodo are standing 2.32 miles apart when they see a hot air balloon floating over their heads. Bilbo’s angle of elevation to the balloon is 28[pic] while Frodo’s angle of elevation to the balloon is 37[pic]. How high up is the balloon?

2. Frodo’s horse can run 20 mph, while Bilbo’s can run 30 mph. After 4 hours, they are 150 miles apart. How far did each person ride? What is the measure of the angle between their paths?

p 2

3. While on a secret mission to save Endor, Leia was put into space to check two satellites. As she approaches the satellites, she finds that one of them is 8 km from her and the other is 11 km. She measures the angle between the two satellites (Leia at the vertex) to be 120[pic]. How far apart are the satellites?

4. Hamlet is storming a castle and needs to find the height of the parapet in order to build scaffolding high enough to go over the walls. From where he is standing, he measures the angle of elevation to be 35[pic]. He moves 50 m closer to the castle and measures the angle of elevation to be 50[pic]. Find the height of the castle walls.

5. A surveyor measures three sides of a triangular field and gets 114 ft, 165 ft, and 257 ft. What is the measure of the largest angle of the triangle?

6. The ramp leading to a bridge must gain 10 feet in elevation. If the angle of elevation of the ramp is to be 3[pic], find the length of the ramp.

7. From the top of a building 25 m high, the angle of elevation of a weather balloon is 54[pic]. From the bottom of the building, the angle of elevation is 61[pic]. How high is the weather balloon?

8. The measures of two sides of a parallelogram are 50 and 80 inches, while one diagonal is 90 inches long. How long is the other diagonal?

9. After signing the treaty in Appomattox, Lee and Grant went their separate ways. Lee traveled SW at 15 mph, while Grant traveled NW at 12 mph. The angle between their paths was 86[pic]. How far apart were Lee and Grant in 2 hours?

P 3

10. Leia has orbited the planet Endor numerous times. .Leia’s postion , satellite A and satellite B form a triangle She determines that the angle at satellite A is 37.4[pic], and the angle at satellite B is 113[pic]. The distance between Leia and satellite A is 5350 km. To the nearest km, how far apart are Leia and the satellite B?

11. Bilbo decides to wage war on the elves, and sends a missile there way. He stands 2 km from the launching pad and observes the missile ascend vertically. After 3 seconds, the angle of elevation between the Bilbo and the missile is 21[pic]. Five seconds later, the angle of elevation is 35[pic]. How far did the missile travel during those 5 seconds?

12. Find the area of a triangle whose sides measure 14 cm, 12 cm and 8 cm.

Homework 11/11. Draw a Picture. Solve. or Right Triangles Trig. Round to two decimal places. Show all work

1. A safety regulation states that the maximum angle of elevation for a rescue ladder is 72˚. A fire department's longest ladder is 110 feet. What is the maximum safe rescue height?

2. At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 35˚, whereas the angle of elevation to the top is 53˚. Find the height of the smokestack alone.

3. A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool is slanted so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep end. Find the angle of depression of the bottom of the pool.

4. For the right triangle given, find all unknown sides and angles.

P 4

5. To avoid a deadly ion cloud, Captain Kirk must steer the Enterprise around it. He turns at an angle of 34[pic] from his original path. He flies for awhile then turns and intercepts his original path at an angle of 28[pic]. He ended up 8 light-years from when he left the path. How far did he travel in order to avoid the ion cloud?

6. In a rush to hurry delivering presents, Santa just drops gifts through the chimney rather than going down himself. Coming upon Mr. Wernau’s house (he’s always good), he measures the angle of depression to be 46[pic] and the line of sight distance is 400 meters. Through a complicated algorithm, Santa knows he must drop the present when the angle of depression is 82[pic]. How much further must Santa travel in order to drop the gift through the chimney?

7. Captain Jack Sparrow is sailing into a harbor at night to avoid detection. His navigator observes a signal buoy at an angle of 15[pic] with the bow of the ship. As Sparrow travels another 1300 meters, the navigator finds that the bouy now makes an angle of 29[pic] with the bow of the ship. How far is the ship from the bouy at the second sighting?

8. A signal flare is seen by two observers, R2-D2 and C3-P0 (who are 5.4 miles apart). R2-D2 observes the angle of elevation to the flare to be 20[pic], while C3-P0 observes the angle of elevation to be 32[pic]. How high up is the flare?

9. After breaking up, Romeo and Juliet ride off in separate directions, “parting is such sweet sorrow.” Romeo rides his horse at 20 mph while Juliet rides her horse at 15 mph. After 3 hours, they are 80 miles apart. Find the angle between their paths?

10. A surveyor measures the lengths of a triangular field to be 25 yds, 38 yds, and 45 yds. What is the measure of the smallest angle in the field?

P 5

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B

C

A

c

a

b=19.4

34˚

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