Welcome to Trigonometry!
|
|
- Naomi Wilkinson
- 5 years ago
- Views:
Transcription
1 Welcome to Trigonometry! Right Triangle Trigonometry: The study of the relationship between the sides and the angles of right triangles.
2 Why is this important? I wonder how tall this cake is feet Or maybe more relevant... I wonder how tall this tree is! 100 m 55 o
3 If we have a right triangle with acute angle A: Opposite means: Across from Adjacent means: Next to A hypotenuse will never be a leg!
4 Opposite A Hypotenuse Adjacent to A Hypotenuse Opposite A Adjacent to A Opposite A Adjacent to A Hypotenuse
5 Hypotenuse Adjacent to A Opposite A Adjacent to A Opposite A Hypotenuse
6 Opposite A Adjacent to A Hypotenuse tangent - The ratio between the length of opposite side to that of the adjacent side.
7 Ex. 1 What is the tangent of angle A? Consider this triangle with angle A approximately 31 o. B 3 A 31 o 5 C What is the tangent of angle A?
8 There is something really cool about right triangles... If the angle is about 31 o, then the tangent (ratio between opposite and adjacent legs) will in fact ALWAYS be about 3 to o o o 9 15 sine the ratio between the length of opposite side to that of the hypotenuse
9 Ex. 2 What is the sine of angle A? cosine The ratio between the length of adjacent side to that of the hypotenuse.
10 Ex. 3 What is the cosine of angle A? To remember which Trig Ratio is which...
11 1. What is the cosine of angle E? 2. What is the sine of angle E?
12 3. What is the tangent of angle E? 4. What is the tangent of B?
13 5. What is the tangent of A? Find the trigonometric value, rounding to four decimal places. sin 52 0 When using trigonometry, it is VERY IMPORTANT that your calculator be in DEGREE MODE! Go to MODE, then down to where it says radian/degree and highlight degree.
14 Find the trigonometric value, rounding to four decimal places. cos 78 0 Find the trigonometric value, rounding to four decimal places. tan 72 0
15 Last chapter, we learned that if we knew the ratio, we could set up a proportion to figure out a missing side in a triangle. 4 x 3 5 This chapter, we're not given similar triangles, but we can find out what the ratio is supposed to be by using our knowledge about trigonometry! 28 o x 15 Look at what sides you have and determine if you need sin, cos, or tan. Then set up the proportion and solve.
16 Ex. 1 Find the missing side length. x 40 o 7 Ex. 2 Find the missing side length. x 40 o 7
17 Ex. 3 Find the missing side length. 40 o x 7 Ex. 4 Find the missing side length. 50 o x 7
18 Ex. 5 Find the missing side length. a o Ex. 6 Find the missing side length o x
19 Ex. 7 Find the missing side length. 25 b 75 o Inverse trig functions: Sin 1, Cos 1, Tan 1 Inverses are used to find the degree measure of an angle. (Sin, Cos and Tan find the side lengths.) An inverse function will negate ("undo") a trig function.
20 Ex. 1 Find θ sin θ =.5567 Round to one decimal place. Ex.2 Find θ tan θ = Round to one decimal place. Goal: Find the measure of angle A. B C What is the tangent of angle A? Then use tan 1 to find the measure of the angle.
21 Ex. 4 What is the measure of angle B? B Ex. 5 What is the measure of angle A? A 8
22 Ex. 6 What is the measure of B angle B? 41 9 Ex. 7 What is the measure of angle C? 15 C 17
23 Ex. 8 Draw a triangle that would match the trig sentence. Then, solve for θ cos θ = 5 12 Ex. 9 Draw a triangle that fits the trig sentence below. Then, find the value of x. Round to one decimal tan 35 ο = x 14
24 Ex. 10 Draw a triangle that fits the trig sentence below. Then, find the value of θ. sin θ ο = Ex. 11 Draw a triangle that fits the trig sentence below. Then, find the value of θ sin θ ο = 17 13
25 Ex. 12 Draw a triangle that fits the trig sentence below. Then, find the value of 0. tan θ ο = Word Problems with Right Triangle Trigonometry
26 Our situation: A girl standing at the bottom of a hill is waving up to her friend who is roasting marshmallows at a campfire on the top of the hill. If the angle of elevation is 27 o and the girl is 200 feet from the bottom of the hill, approximately how tall is the hill? Angle of Depression Horizontal Angle of Elevation Horizontal Hill Formal Definitions: Angle of Elevation: If you are looking up, it is the angle from the horizontal UP to the line of sight. Angle of Depression: If you are looking down, it is the angle from the horizontal DOWN to the line of sight.
27 What conjecture can you make about the angles of elevation and depression? Think about parallel lines... Angle of Depression Angle of Elevation The angle of elevation from a sailboat to the top of a 121 foot lighthouse on the shore is 16 degrees. To the nearest foot, how far is the sailboat from the shore? Step 1: Draw a picture Step 2: Decide sin, cos or tan Step 3: Solve
28 Ex. 2) A helicopter is hovering over a landing pad 100 meters from where you are standing. The helicopter s angle of elevation with the ground is 12 o. What is the altitude of the helicopter? Ex. 3) Ray, a lighthouse operator sits in the top of his lighthouse 25 meters above sea level. He sights a sailboat in the distance. The angle of depression of the sighting is 10 o. How far is the boat from the base of the lighthouse? Give your answer to the nearest 10 meters.
29 Ex. 4) You are flying a kite and let out 240 feet of string. The kite s angle of elevation with the ground is If the string is stretched straight, how high is the kite above the ground? Homework: 13.1 Page 647#1-5, 7-17 odd, Page 650 1, 2, 3-17 odd, 18-23
Put in simplest radical form. (No decimals)
Put in simplest radical form. (No decimals) 1. 2. 3. 4. 5. 6. 5 7. 4 8. 6 9. 5 10. 9 11. -3 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 3 28. 1 Geometry Chapter 8 - Right Triangles
More information8.3 Trigonometric Ratios-Tangent. Geometry Mr. Peebles Spring 2013
8.3 Trigonometric Ratios-Tangent Geometry Mr. Peebles Spring 2013 Bell Ringer 3 5 Bell Ringer a. 3 5 3 5 = 3 5 5 5 Multiply the numerator and denominator by 5 so the denominator becomes a whole number.
More informationLearning Goal: I can explain when to use the Sine, Cosine and Tangent ratios and use the functions to determine the missing side or angle.
MFM2P Trigonometry Checklist 1 Goals for this unit: I can solve problems involving right triangles using the primary trig ratios and the Pythagorean Theorem. U1L4 The Pythagorean Theorem Learning Goal:
More informationChapter 7. Right Triangles and Trigonometry
Chapter 7 Right Triangles and Trigonometry 4 16 25 100 144 LEAVE IN RADICAL FORM Perfect Square Factor * Other Factor 8 20 32 = = = 4 *2 = = = 75 = = 40 = = 7.1 Apply the Pythagorean Theorem Objective:
More informationI can add vectors together. IMPORTANT VOCABULARY
Pre-AP Geometry Chapter 9 Test Review Standards/Goals: G.SRT.7./ H.1.b.: I can find the sine, cosine and tangent ratios of acute angles given the side lengths of right triangles. G.SRT.8/ H.1.c.: I can
More informationA life not lived for others is not a life worth living. Albert Einstein
life not lived for others is not a life worth living. lbert Einstein Sides adjacent to the right angle are legs Side opposite (across) from the right angle is the hypotenuse. Hypotenuse Leg cute ngles
More informationModule 13 Trigonometry (Today you need your notes)
Module 13 Trigonometry (Today you need your notes) Question to ponder: If you are flying a kite, you know the length of the string, and you know the angle that the string is making with the ground, can
More informationApplication of Geometric Mean
Section 8-1: Geometric Means SOL: None Objective: Find the geometric mean between two numbers Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse
More informationApplying Trigonometry: Angles of Depression and Elevation
Applying Trigonometry: Angles of Depression and Elevation An angle of elevation is the angle formed by a horizontal line and the line of sight to a point above. In the diagram, 1 is the angle of elevation.
More informationChapter 8: Right Triangles (page 284)
hapter 8: Right Triangles (page 284) 8-1: Similarity in Right Triangles (page 285) If a, b, and x are positive numbers and a : x = x : b, then x is the between a and b. Notice that x is both in the proportion.
More informationSin, Cos, and Tan Revealed
Sin, Cos, and Tan Revealed Reference Did you ever wonder what those keys on your calculator that say sin, cos, and tan are all about? Well, here s where you find out. You ve seen that whenever two right
More informationUnit 2: Right Triangle Trigonometry RIGHT TRIANGLE RELATIONSHIPS
Unit 2: Right Triangle Trigonometry This unit investigates the properties of right triangles. The trigonometric ratios sine, cosine, and tangent along with the Pythagorean Theorem are used to solve right
More information1. A right triangle has legs of 8 centimeters and 13 centimeters. Solve the triangle completely.
9.7 Warmup 1. A right triangle has legs of 8 centimeters and 13 centimeters. Solve the triangle completely. 2. A right triangle has a leg length of 7 in. and a hypotenuse length of 14 in. Solve the triangle
More informationUNIT 2 RIGHT TRIANGLE TRIGONOMETRY Lesson 2: Applying Trigonometric Ratios Instruction
Prerequisite Skills This lesson requires the use of the following skills: defining and calculating sine, cosine, and tangent setting up and solving problems using the Pythagorean Theorem identifying the
More informationTrig Functions Learning Outcomes. Solve problems about trig functions in right-angled triangles. Solve problems using Pythagoras theorem.
1 Trig Functions Learning Outcomes Solve problems about trig functions in right-angled triangles. Solve problems using Pythagoras theorem. Opposite Adjacent 2 Use Trig Functions (Right-Angled Triangles)
More informationWeek 11, Lesson 1 1. Warm Up 2. Notes Sine, Cosine, Tangent 3. ICA Triangles
Week 11, Lesson 1 1. Warm Up 2. Notes Sine, Cosine, Tangent 3. ICA Triangles HOW CAN WE FIND THE SIDE LENGTHS OF RIGHT TRIANGLES? Essential Question Essential Question Essential Question Essential Question
More informationStudent Instruction Sheet: Unit 4, Lesson 4. Solving Problems Using Trigonometric Ratios and the Pythagorean Theorem
Student Instruction Sheet: Unit 4, Lesson 4 Suggested Time: 75 minutes Solving Problems Using Trigonometric Ratios and the Pythagorean Theorem What s important in this lesson: In this lesson, you will
More informationOVERVIEW Similarity Leads to Trigonometry G.SRT.6
OVERVIEW Similarity Leads to Trigonometry G.SRT.6 G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric
More informationBASICS OF TRIGONOMETRY
Mathematics Revision Guides Basics of Trigonometry Page 1 of 9 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier BASICS OF TRIGONOMETRY Version: 1. Date: 09-10-015 Mathematics Revision
More informationUnit 3 Trigonometry. 3.1 Use Trigonometry to Find Lengths
Topic : Goal : Unit 3 Trigonometry trigonometry I can use the primary trig ratios to find the lengths of sides in a right triangle 3.1 Use Trigonometry to Find Lengths In any right triangle, we name the
More informationTrig Functions Learning Outcomes. Solve problems about trig functions in right-angled triangles. Solve problems using Pythagoras theorem.
1 Trig Functions Learning Outcomes Solve problems about trig functions in right-angled triangles. Solve problems using Pythagoras theorem. Opposite Adjacent 2 Use Trig Functions (Right-Angled Triangles)
More informationGeom- Chpt. 8 Algebra Review Before the Chapter
Geom- Chpt. 8 Algebra Review Before the Chapter Solving Quadratics- Using factoring and the Quadratic Formula Solve: 1. 2n 2 + 3n - 2 = 0 2. (3y + 2) (y + 3) = y + 14 3. x 2 13x = 32 1 Working with Radicals-
More informationWhen Solving for a LEG or HYPOTENUSE of the right triangle, When solving for one of the complementary ANGLES of the right triangle, use
What should be labeled in the triangle? How do we remember the formulas? When Solving for a LEG or HYPOTENUSE of the right triangle, use When solving for one of the complementary ANGLES of the right triangle,
More informationLesson 30, page 1 of 9. Glencoe Geometry Chapter 8.3. Trigonometric Ratios
Lesson 30 Lesson 30, page 1 of 9 Glencoe Geometry Chapter 8.3 Trigonometric Ratios Today we look at three special ratios of right triangles. The word Trigonometry is derived from two Greek words meaning
More informationMBF3C: Mathematics of Personal Finance. Angle of elevation (inclination) is the angle made between the and the line of sight to an object.
Angle of elevation (inclination) is the angle made between the and the line of sight to an object. Angle of depression is the angle made between the and the line of sight to an object. Example 1: A wheelchair
More informationUse SOH CAH TOA to memorize the three main trigonometric functions.
Use SOH CAH TOA to memorize the three main trigonometric functions. Content Objective Content Objective Content Objective Content Objective Content Objective Content Objective Content Objective Content
More informationSecondary 3 Mathematics Chapter 10 Applications of Trigonometry Practice 1 Learning Objectives: To provide an aim for
1 1 1 1 1 1 1 1 1 1 Secondary 3 Mathematics Chapter pplications of Trigonometry Practice 1 Learning Objectives: To provide an aim for students to achieve at the end of each lesson. Understand and solve
More informationReview on Right Triangles
Review on Right Triangles Identify a Right Triangle Example 1. Is each triangle a right triangle? Explain. a) a triangle has side lengths b) a triangle has side lengths of 9 cm, 12 cm, and 15 cm of 5 cm,7
More informationMarch 01, Applications of Rt triangle trig ink.notebook. 8.4 Applications of Rt Triangle Trig. Standards
Lesson Objectives Standards Lesson Notes Lesson Objectives Standards Lesson Notes 8.4 Applications of Rt Triangle Trig After this lesson, you should be able to successfully find and use trigonometric ratios
More informationMath Section 4.1 Special Triangles
Math 1330 - Section 4.1 Special Triangles In this section, we ll work with some special triangles before moving on to defining the six trigonometric functions. Two special triangles are 30 60 90 triangles
More informationSimilar Right Triangles
MATH 1204 UNIT 5: GEOMETRY AND TRIGONOMETRY Assumed Prior Knowledge Similar Right Triangles Recall that a Right Triangle is a triangle containing one 90 and two acute angles. Right triangles will be similar
More informationFunctions - Trigonometry
10. Functions - Trigonometry There are si special functions that describe the relationship between the sides of a right triangle and the angles of the triangle. We will discuss three of the functions here.
More informationThe study of the measurement of triangles is called Trigonometry.
Math 10 Workplace & Apprenticeship 7.2 The Sine Ratio Day 1 Plumbers often use a formula to determine the lengths of pipes that have to be fitted around objects. Some common terms are offset, run, and
More information84 Geometric Mean (PAAP and HLLP)
84 Geometric Mean (PAAP and HLLP) Recall from chapter 7 when we introduced the Geometric Mean of two numbers. Ex 1: Find the geometric mean of 8 and 96.ÿ,. dÿ,... : J In a right triangle, an altitude darn
More informationEQ: SRT.8 How do I use trig to find missing side lengths of right triangles?
EQ: SRT.8 How do I use trig to find missing side lengths of right triangles? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential
More information8-1. The Pythagorean Theorem and Its Converse. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
8-1 The Pythagorean Theorem and Its Converse Vocabulary Review 1. Write the square and the positive square root of each number. Number 9 Square Positive Square Root 1 4 1 16 Vocabulary Builder leg (noun)
More informationChapter 3: Trigonometry
: Unit 3&4 - Trigonometry Chapter 3: Trigonometry 3.10 Sine or Cosine? Sine Law Cosine Law ASA or AAS SAS ASS SSS Example #1: 12 70 9 Example #2: 17 35 14 1) 2) 3) Solve each triangle ABC. Round answers
More informationEQ: How do I use trigonometry to find missing side lengths of right triangles?
EQ: How do I use trigonometry to find missing side lengths of right triangles? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential
More information8-1. The Pythagorean Theorem and Its Converse. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
8-1 he Pythagorean heorem and Its Converse Vocabulary Review 1. Write the square and the positive square root of each number. Number Square Positive Square Root 9 81 3 1 4 1 16 1 2 Vocabulary Builder leg
More information1 What is Trigonometry? Finding a side Finding a side (harder) Finding an angle Opposite Hypotenuse.
Trigonometry (9) Contents 1 What is Trigonometry? 1 1.1 Finding a side................................... 2 1.2 Finding a side (harder).............................. 2 1.3 Finding an angle.................................
More information8.7 Extension: Laws of Sines and Cosines
www.ck12.org Chapter 8. Right Triangle Trigonometry 8.7 Extension: Laws of Sines and Cosines Learning Objectives Identify and use the Law of Sines and Cosines. In this chapter, we have only applied the
More informationParking Lot HW? Joke of the Day: What do you get when you combine a flat, infinite geometric figure with a beef patty?
Parking Lot HW? Joke of the Day: What do you get when you combine a flat, infinite geometric figure with a beef patty? a plane burger Agenda 1 23 hw? Finish Special Right Triangles L8 3 Trig Ratios HW:
More informationHonors Geometry Chapter 8 Test Review
Honors Geometry Chapter 8 Test Review Name Find the geometric mean between each pair of numbers. 1. 9 and 14 2. 20 and 80 3. 8 2 3 and 4 2 3 4. Find x, y and z. 5. Mike is hanging a string of lights on
More informationUnit #8 Review Right Triangle Trigonometry. 1. Which of the following could represent the sides of a right triangle?
Name: Date: Unit #8 Review Right Triangle Trigonometry 1. Which of the following could represent the sides of a right triangle? (1) { 6, 8,14 } (2) {, 20, } (3) { 15, 20, } (4) {,15, 20 } 2. Which of the
More informationGeometry Chapter 7 Review Right Triangles Use this review to help prepare for the Chapter 7 Test. The answers are attached at the end of the document.
Use this review to help prepare for the hapter 7 Test. The answers are attached at the end of the document. 1. Solve for a and b. 2. Find a, b, and h. 26 24 a h b 10 b a 4 12. The tangent of is. 4. A is
More informationThe Battleship North Carolina s Fire Control
The Battleship North Carolina s Fire Control Objectives: 1. Students will see the application of trigonometry that the Mark 14 gun sight used with the 20mm guns aboard the NC Battleship. (Geometry SCOS:
More informationTest Review: Geometry I Period 2,4,6. TEST DATE: All classes Wednesday April 9. Things it would be a good idea to know:
Test Review: Geometry I Period 2,4,6 TEST DATE: All classes Wednesday April 9 Things it would be a good idea to know: 1) Special Right Triangles 2) Geometric Mean 3) SOHCAHTOA Test Outline Part I - Non-Calculator
More information77.1 Apply the Pythagorean Theorem
Right Triangles and Trigonometry 77.1 Apply the Pythagorean Theorem 7.2 Use the Converse of the Pythagorean Theorem 7.3 Use Similar Right Triangles 7.4 Special Right Triangles 7.5 Apply the Tangent Ratio
More informationWord problems introduce two new vocabulary terms:
Worksheet 1-3: Angle of Elevation vs. Angle of Depression Trigonometry is used on a daily basis in the workplace. Since trigonometry means "triangle measure", any profession that deals with measurement
More informationAlgebra/Geometry Blend Unit #7: Right Triangles and Trigonometry Lesson 1: Solving Right Triangles. Introduction. [page 1]
Algebra/Geometry Blend Unit #7: Right Triangles and Trigonometry Lesson 1: Solving Right Triangles Name Period Date Introduction [page 1] Learn [page 2] Pieces of a Right Triangle The map Brian and Carla
More informationChapter 3: Trigonometry !! =!! +!!!"#!"#$
3.11 Sine or Cosine Word Problems Chapter 3: Trigonometry Basic Trig Ratios Geometry Rules!"#!"#!"#!"#$%&!"!!"#$%&'( =!"# Sine Law Cosine Law!!"#! =!!"#! =!!"#!!! =!! +!!!"#!"#$ Example #1 Two security
More information8-5 Angles of Elevation and Depression
4. HOCKEY A hockey player takes a shot 20 feet away from a 5-foot goal. If the puck travels at a angle of elevation toward the center of the goal, will the player score? 5. MOUNTAINS Find the angle of
More informationRiverboat and Airplane Vectors
Grade Homework Riverboat and Airplane Vectors It all depends on your point of view It s all relative On occasion objects move within a medium that is moving with respect to an observer. In such instances,
More informationMORE TRIGONOMETRY
MORE TRIGONOMETRY 5.1.1 5.1.3 We net introduce two more trigonometric ratios: sine and cosine. Both of them are used with acute angles of right triangles, just as the tangent ratio is. Using the diagram
More informationRight-angled triangles and trigonometry
Right-angled triangles and trigonometry 5 syllabusref Strand: Applied geometry eferenceence Core topic: Elements of applied geometry In this cha 5A 5B 5C 5D 5E 5F chapter Pythagoras theorem Shadow sticks
More informationAP Physics 1 Summer Packet Review of Trigonometry used in Physics
AP Physics 1 Summer Packet Review of Trigonometry used in Physics For some of you this material will seem pretty familiar and you will complete it quickly. For others, you may not have had much or any
More informationIn previous examples of trigonometry we were limited to right triangles. Now let's see how trig works in oblique (not right) triangles.
The law of sines. In previous examples of trigonometry we were limited to right triangles. Now let's see how trig works in oblique (not right) triangles. You may recall from Plane Geometry that if you
More informationRight is Special 1: Triangles on a Grid
Each student in your group should have a different equilateral triangle. Complete the following steps: Using the centimeter grid paper, determine the length of the side of the triangle. Write the measure
More informationApplications of trigonometry
Applications of trigonometry This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More informationSection 8: Right Triangles
The following Mathematics Florida Standards will be covered in this section: MAFS.912.G-CO.2.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition
More informationUnit 2 Day 4 Notes Law of Sines
AFM Unit 2 Day 4 Notes Law of Sines Name Date Introduction: When you see the triangle below on the left and someone asks you to find the value of x, you immediately know how to proceed. You call upon your
More informationTopic 15 - Guided Assessment#1-10 & More Practice #1-10 Jan 28 - Jan 31, 2014
2/0/4 2:8 PM Topic 5 - Guie Assessment#-0 & More Practice #-0 Jan 28 - Jan 3, 204 Teacher: Melva Yazzie Topic 5 - Guie Assessment#-0 & More Practice #-0 5. Right triangle an trig relationships Course:
More informationThe statements of the Law of Cosines
MSLC Workshop Series: Math 1149 and 1150 Law of Sines & Law of Cosines Workshop There are four tools that you have at your disposal for finding the length of each side and the measure of each angle of
More informationPre-Calculus Nov. 14 th to Nov. 27 th 2012 Unit 6 Triangle Trigonometry. Date Topic Assignment Did It
Pre-Calculus Nov. 14 th to Nov. 27 th 2012 Unit 6 Triangle Trigonometry Date Topic Assignment Did It Wednesday 11/14 Thursday 11/15 Friday 11/16 Monday 11/19 Tuesday 11/20 4.3 Right Triangle Trigonometry
More informationTrigonometry. terminal ray
terminal ray y Trigonometry Trigonometry is the study of triangles the relationship etween their sides and angles. Oddly enough our study of triangles egins with a irle. r 1 θ osθ P(x,y) s rθ sinθ x initial
More informationLearning Objectives Source/Example Questions
Grade and Strand Learning Objectives Source/Example Questions.ca Ascent Education: http://questions.ascenteducatio n.com.ca A tree 66 meters high casts a 44-meter shadow. Find the angle of elevation of
More informationA2.A.73: Law of Sines 4: Solve for an unknown side or angle, using the Law of Sines or the Law of Cosines
A2.A.73: Law of Sines 4: Solve for an unknown side or angle, using the Law of Sines or the Law of Cosines 1 In the accompanying diagram of ABC, m A = 65, m B = 70, and the side opposite vertex B is 7.
More information4.8/5.5/5.6 Right Triangle Trig Applications Law of Sines & Law of Cosines
Objective: 4.8/5.5/5.6 Right Triangle Trig Applications Law of Sines & Law of Cosines Apply right triangle trigonometry. Solve triangles using the Law of Sines and the Law of Cosines. WARMUP Find the missing
More informationMath 20-3 Admission Exam Study Guide Notes about the admission exam:
Math 20-3 Admission Exam Study Guide Notes about the admission exam: To write the exam, no appointment is necessary; drop-in to MC221 (Testing) and ask for the 20-3 exam. You ll be given a form to take
More information3.1. The Tangent Ratio. 100 MHR Chapter 3
3.1 The Tangent Ratio Focus on explaining the relationships between similar triangles and the definition of the tangent ratio identifying the hypotenuse, opposite side, and side for a given acute angle
More informationLesson 5. Section 2.2: Trigonometric Functions of an Acute Angle 1 = 1
Lesson 5 Diana Pell March 6, 2014 Section 2.2: Trigonometric Functions of an Acute Angle 1 = 1 360 We can divide 1 into 60 equal parts, where each part is called 1 minute, denoted 1 (so that 1 minute is
More informationWarm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up
Solve applied problems using the attributes of similar triangles. Solve problems using ratio and proportions. Investigate the fundamental concepts behind trigonometry: three basic trig functions and how
More informationUnit 7 Trigonometry Test #1 Review
Secondary Math 3 Name x 2^0Y1T9l NKYu]tga\ gsgovfztywdamr]e _LYLrg.n j HDlRls TrgiUgMhntvsZ TryedsUearbverdz. Unit 7 Trigonometry Test #1 Review Find the value of the trig function indicated. Date Period
More information*Definition of Cosine
Vetors - Unit 3.3A - Problem 3.5A 3 49 A right triangle s hypotenuse is of length. (a) What is the length of the side adjaent to the angle? (b) What is the length of the side opposite to the angle? ()
More informationTrigonometry. What you will learn
C H P T R 10 Trigonometry hat you will learn 10.1 Introducing trigonometry 10.2 Finding the side length of a right-angled triangle 10.3 Further problems involving side lengths 10.4 Finding the angle 10.5
More informationTrigonometric Functions
Trigonometric Functions (Chapters 6 & 7, 10.1, 10.2) E. Law of Sines/Cosines May 21-12:26 AM May 22-9:52 AM 1 degree measure May 22-9:52 AM Measuring in Degrees (360 degrees) is the angle obtained when
More informationParallel Lines Cut by a Transversal
Name Date Class 11-1 Parallel Lines Cut by a Transversal Parallel Lines Parallel Lines Cut by a Transversal A line that crosses parallel lines is a transversal. Parallel lines never meet. Eight angles
More informationChapter 4 Pre-Test Review
--"'fl Name Per Date _ Chapter 4 Pre-Test Review 1. Find the value of the variable in the triangles below. Give an eact answer and a decimal approimation. 9 13 10 12 2. Given the area of the triangles
More informationAP Physics B Summer Homework (Show work)
#1 NAME: AP Physics B Summer Homework (Show work) #2 Fill in the radian conversion of each angle and the trigonometric value at each angle on the chart. Degree 0 o 30 o 45 o 60 o 90 o 180 o 270 o 360 o
More information5.8. Solving Three-Dimensional Problems by Using Trigonometry. LEARN ABOUT the Math. Matt s Solution. 328 Chapter 5
YOU WILL NEE dynamic geometry software (optional) Solving Tree-imensional Problems by Using Trigonometry GOL Solve tree-dimensional problems by using trigonometry. LERN OUT te Mat From point, Manny uses
More informationTRAINING LAB BLOOD AS EVIDENCE BLOOD DROPS FALLING AT AN ANGLE NAME
TRAINING LAB BLOOD AS EVIDENCE BLOOD DROPS FALLING AT AN ANGLE NAME Background: You just completed studying the behavior of passive blood drops that drip straight down from a wound, but not all blood drops
More informationCalculus 12: Evaluation 3 Outline and Review
Calculus 12: Evaluation 3 Outline and Review You should be able to: 1. Differentiate various types of functions including trigonometric, exponential and logarithmic functions, 2. Solve various related
More informationDate Lesson Assignment Did it grade Friday Feb.24
PAP Pre-Calculus Lesson Plans Unit Sem 2 3 rd term Johnston (C4) and Noonan (C6) February 24 th to March 9 th 202 - Vectors Date Lesson Assignment Did it grade Friday Feb.24 Law of Sines/Cosines, Area
More informationG.SRT.C.8: Using Trigonometry to Find a Side 3
Regents Exam Questions www.jmap.org Name: 1 The tailgate of a truck is 2 feet above the ground. The incline of a ramp used for loading the truck is 11, as shown below. 3 Find, to the nearest tenth of a
More informationChapter 3 &4_2015.notebook March 09, 2018
Example 2 John wants to measure the length of the trunk of a tree. He walks exactly 35 m from the base of the tree, he lays down and looks up to the top of the tree. The angle from the ground to the top
More informationMath at Work 11: Chapter 7. February 20, 2012, 17:00
Math at Work 11: Chapter 7 February 20, 2012, 17:00 Keith operates a large crane. He must lift building materials over the houses from the street, and set them down in the work site. He must be sure that
More informationPythagorean Theorem Name:
Name: 1. A wire reaches from the top of a 13-meter telephone pole to a point on the ground 9 meters from the base of the pole. What is the length of the wire to the nearest tenth of a meter? A. 15.6 C.
More informationSpecial Right Triangle Task Cards
Special Right Triangle Task Cards 45-45-90 and 30-60-90 Special Right Triangle Task Cards 45-45-90 and 30-60-90 Teachers: I have included 2 sets of task cards. The first set (slides 3-9) asks for the answer
More information8.1 The Law of Sines Congruency and Oblique Triangles Using the Law of Sines The Ambiguous Case Area of a Triangle
Chapter 8 Applications of Trigonometry 8-1 8.1 The Law of Sines Congruency and Oblique Triangles Using the Law of Sines The Ambiguous Case Area of a Triangle A triangle that is not a right triangle is
More informationmath lib activity Created by: ALL THINGS ALGEBRA
math lib activity Created by: ALL THINGS ALGEBRA Angle of Elevation & Depression Math Lib Activity! Objective: To practice solving problems that relate the angle of elevation and depression. Students must
More informationTitle: Direction and Displacement
Title: Direction and Displacement Subject: Mathematics Grade Level: 10 th 12 th Rational or Purpose: This activity will explore students knowledge on directionality and displacement. With the use angle
More informationCCM8 Unit 7: Pythagorean Theorem Vocabulary
CCM8 Unit 7: Pythagorean Theorem Vocabulary Base Exponent Hypotenuse Legs Perfect Square Pythagorean Theorem When a number is raised to a power, the number that is used as a factor The number that indicates
More informationStudy Island. Generation Date: 04/01/2014 Generated By: Cheryl Shelton Title: 10th Grade Geometry Right Angle Trig
Study Island Copyright 2014 Edmentum - All rights reserved. Generation Date: 04/01/2014 Generated By: Cheryl Shelton Title: 10th Grade Geometry Right Angle Trig 1. A lamp illuminates an area that is 12
More informationRelated Rates - Classwork
Related Rates - Classwork Earlier in the year, we used the basic definition of calculus as the mathematics of change. We defined words that meant change: increasing, decreasing, growing, shrinking, etc.
More informationUnit 6: Pythagorean Theorem. 1. If two legs of a right triangle are 9 and 11, the hypotenuse is
Name: ate: 1. If two legs of a right triangle are 9 and 11, the hypotenuse is 7. Triangle A is a right triangle with legs that measure 7 and 8. The length of the hypotenuse is 20. 2. 40. 202 15. 113. 9.
More informationChp. 3_4 Trigonometry.notebook. October 01, Warm Up. Pythagorean Triples. Verifying a Pythagorean Triple... Pythagorean Theorem
Chp. 3_4 Trigonometry.noteook Wrm Up Determine the mesure of the vrile in ech of the following digrms: x + 2 x x 5 x + 3 Pythgoren Theorem - is fundmentl reltionship mongst the sides on RIGHT tringle.
More informationTwo-Dimensional Motion and Vectors
Science Objectives Students will measure and describe one- and two-dimensional position, displacement, speed, velocity, and acceleration over time. Students will graphically calculate the resultant of
More informationGary Delia AMS151 Fall 2009 Homework Set 3 due 10/07/2010 at 11:59pm EDT
Gary Delia AMS151 Fall 2009 Homework Set 3 due 10/07/2010 at 11:59pm EDT 1. (2 pts) The angle of elevation to the top of a building is found to be 9 from the ground at a distance of 6000 feet from the
More informationMath-3. Lesson 6-5 The Law of Sines The Ambiguous Case
Math-3 Lesson 6-5 The Law of Sines The miguous Case Quiz 6-4: 1. Find the measure of angle θ. Ө = 33.7 2. What is the cosecant ratio for ϴ? Csc Ө = 2 5 5 3. standard position angle passes through the point
More information4-7 The Law of Sines and the Law of Cosines
Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree. 27. ABC, if A = 42, b = 12, and c = 19 Use the Law of Cosines to find the missing side measure. Use
More information