|
|
- Jasmin Warren
- 6 years ago
- Views:
Transcription
1 Algebra Lab Investigating Trigonometri Ratios You an use paper triangles to investigate the ratios of the lengths of sides of right triangles. Virginia SOL Preparation for G.8 The student will solve realworld problems involving right triangles by using the Pythagorean Theorem and its onverse, properties of speial right triangles, and right triangle trigonometry. Ativity Collet the Data Step 1 Use a ruler and grid paper to draw several right triangles with legs in a ratio of :8. Inlude right triangles with the side lengths listed in the table below and several more right triangles similar to these three. Label the verties of eah triangle as A, B, and C, where C is at the right angle, B is opposite the longest leg, and A is opposite the shortest leg. A 16 Step 2 Copy the table below. Complete the first three olumns by measuring the hypotenuse (side AB ) in eah right triangle you reated and reording its length to the nearest tenth. C 10 B Step Calulate and reord the ratios in the middle two olumns. Round to the nearest hundredth. Step 4 Use a protrator to arefully measure angles A and B to the nearest degree in eah right triangle. Reord the angle measures in the table. Side Lengths Ratios Angle Measures side BC side AC side AB _ BC _ BC angle A angle B angle C AC AB Analyze the Results 1. Examine the measures and ratios in the table. What do you notie? Write a sentene or two to desribe any patterns you see. Make a Conjeture 2. For any right triangle similar to the ones you have drawn here, what will be the value of the ratio of the length of the shortest leg to the length of the longest leg?. If you draw a right triangle and alulate the ratio of the length of the shortest leg to the length of the hypotenuse to be approximately 0., what will be the measure of the larger aute angle in the right triangle? x=? 648 Explore 10-8 Algebra Lab: Investigating Trigonometri Ratios
2 Trigonometri Ratios Then You used the Pythagorean Theorem (Lesson 10-) Now 1Find trigonometri ratios of angles. 2Use trigonometry to solve triangles. Why? If a road has a perent grade of 8%, this means the road rises or falls 8 feet over a horizontal distane of 100 feet. Trigonometri ratios an be used to determine the angle that the road rises or falls. New Voabulary trigonometry trigonometri ratio sine osine tangent solving the triangle inverse sine inverse osine inverse tangent Trigonometri Ratios Trigonometry is the study of relationships among the 1 angles and sides of triangles. A trigonometri ratio is a ratio that ompares the side lengths of two sides of a right triangle. The three most ommon trigonometri ratios, sine, osine, and tangent, are desribed below. Key Conept Trigonometri Ratios leg opposite A sine of A = hypotenuse Words Symbols Model sin A = a _ A leg adjaent to A osine of A = hypotenuse os A = b _ b Virginia i SOL Preparation for G.8 The student will solve real-world problems involving right triangles by using the Pythagorean Theorem and its onverse, properties of speial right triangles, and right triangle trigonometry. leg opposite A tangent of A = Leg adjaent to A tan A = a _ b Opposite, adjaent, and hypotenuse are abbreviated opp, adj, and hyp, respetively Example 1 Find Sine, Cosine, and Tangent Ratios Find the values of the three trigonometri ratios for angle A. Step 1 Use the Pythagorean Theorem to find b. a 2 + b 2 = 2 Pythagorean Theorem Step b 2 = 1 2 a = 9 and = b 2 = 22 Simplify. b 2 = 144 b = 12 Subtrat 81 from eah side. Take the square root of eah side. Use the side lengths to write the trigonometri ratios. sin A = _ opp hyp = _ 9 1 = _ os A = _ adj hyp = _ 12 1 = 4_ tan A = _ opp adj 9 C b a 1 B = _ 9 12 = _ 4 GuidedPratie 1. Find the values of the three trigonometri ratios for angle B. onneted.mgraw-hill.om 649
3 Wath Out! Calulator Mode Make sure your graphing alulator is in degree mode. Example 2 Use a Calulator to Evaluate Expressions Use a alulator to find os 42 to the nearest ten-thousandth. KEYSTROKES: 42 Rounded to the nearest ten-thousandth, os GuidedPratie 2A. sin 1 2B. tan 6 2C. os Use Trigonometri Ratios When you find all unknown measures of the sides 2 and angles of a right triangle, you are solving the triangle. You an find the missing measures if you know the measure of two sides of the triangle or the measure of one side and the measure of one aute angle. Example Solve a Triangle Solve the right triangle. Round eah side length to the nearest tenth. 6 Study Tip Remembering Trigonometri Ratios SOH CAH TOA an be used to help you remember the ratios for sine, osine, and tangent. Eah letter represents a word. sin A = _ opp hyp os A = _ adj hyp tan A = _ opp adj Step 1 Find the measure of A ( ) = 49 The measure of A = 49. Step 2 Find a. Sine you are given the measure of the side opposite B and are finding the measure of the side adjaent to B, use the tangent ratio. tan 41 = 6 _ a Definition of tangent a tan 41 = 6 Multiply eah side by a. a = 6_ or about 6.9 tan 41 So the measure of a or BC is about 6.9. a 41 Divide eah side by tan 41. Use a alulator. Step Find. Sine you are given the measure of the side opposite B and are finding the measure of the hypotenuse, use the sine ratio. sin 41 = 6 _ Definition of sine sin 41 = 6 Multiply eah side by. = 6_ or about 9.1 sin 41 So the measure of or AB is about 9.1. Divide eah side by sin 41. Use a alulator. GuidedPratie A. B Lesson 10-8 Trigonometri Ratios
4 Real-World Example 4 Find a Missing Side Length EXERCISE A trainer sets the inline on a treadmill to 10. The walking surfae of the treadmill is feet long. About how many inhes is the end of the treadmill from the floor? sin 10 = _ h ft h Definition of sine sin 10 = h Multiply eah side by. 0.8 h Use a alulator. The value of h is in feet. Multiply 0.8 by 12 to onvert feet to inhes. The trainer raised the treadmill about 10.4 inhes. 10 Real-World Link For optimum health, all adults ages 18 6 should get at least 0 minutes of moderately intense ativity five days per week. Soure: Amerian Heart Assoiation GuidedPratie 4. SKATEBOARDING The angle that a skateboarding ramp forms with the ground is 2 and the height of the ramp is 6 feet. Determine the length of the ramp. A trigonometri funtion has a rule given by a trigonometri ratio. If you know the sine, osine, or tangent of an aute angle, you an use the inverse of the trigonometri funtion to find the measure of the angle. Key Conept Inverse Trigonometri Funtions Words If A is an aute angle and the sine of A is x, then the inverse sine of x is the measure of A. Symbols Words Symbols Words Symbols If sin A = x, then sin -1 x = m A. If A is an aute angle and the osine of A is x, then the inverse osine of x is the measure of A. If os A = x, then os -1 x = m A. If A is an aute angle and the tangent of A is x, then the inverse tangent of x is the measure of A. If tan A = x, then tan -1 x = m A. Example Find a Missing Angle Measure Find m Y to the nearest degree. You know the measure of the side adjaent to Y and 19 the measure of the hypotenuse. Use the osine ratio. 8 os Y = _ 8 Definition of osine 19 Use a alulator and the [CO S -1 ] funtion to find the measure of the angle. KEYSTROKES: [CO S -1 ] So, m Y = 6. GuidedPratie. Find m X to the nearest degree if XY = 14 and YZ =. onneted.mgraw-hill.om 61
5 Chek Your Understanding = Step-by-Step Solutions begin on page R12. Example 1 Find the values of the three trigonometri ratios for angle A Example 2 Example Use a alulator to find the value of eah trigonometri ratio to the nearest ten-thousandth.. sin 6. os 2. tan os 82 Solve eah right triangle. Round eah side length to the nearest tenth Example 4 1. SNOWBOARDING A hill used for snowboarding has a vertial drop of 00 feet. The angle the run makes with the ground is 18. Estimate the length of r. 00 ft r 18 Example Find m X for eah right triangle to the nearest degree Lesson 10-8 Trigonometri Ratios
6 Pratie and Problem Solving Extra Pratie begins on page 81. Example 1 Find the values of the three trigonometri ratios for angle B Example 2 Use a alulator to find the value of eah trigonometri ratio to the nearest ten-thousandth. 21. tan sin os tan 4 Example 2. sin 26. os sin tan 60 Solve eah right triangle. Round eah side length to the nearest tenth Example 4. ESCALATORS At a loal mall, an esalator is 110 feet long. The angle the esalator makes with the ground is 29. Find the height reahed by the esalator. 110 ft h 29 Example Find m J for eah right triangle to the nearest degree B 42. MONUMENTS The Linoln Memorial building measures 204 feet long, 14 feet wide, and 99 feet tall. Chloe is looking at the top of the monument at an angle of. How far away is she standing from the monument? onneted.mgraw-hill.om 6
7 4 AIRPLANES Ella looks down at a ity from an airplane window. The airplane is 000 feet in the air, and she looks down at an angle of 8. Determine the horizontal distane to the ity. 44. FORESTS A forest ranger estimates the height of a tree is about 1 feet. If the forest ranger is standing 100 feet from the base of the tree, what is the measure of the angle formed by the ranger and the top of the tree? Suppose A is an aute angle of right triangle ABC. 4. Find sin A and tan A if os A = _ Find tan A and os A if sin A = 2_. 4. Find os A and tan A if sin A = 1_ Find sin A and os A if tan A = _. 49. SUBMARINES A submarine desends into the oean at an angle of 10 below the water line and travels miles diagonally. How far beneath the surfae of the water has the submarine reahed? C 0. MULTIPLE REPRESENTATIONS In this problem, you will explore a relationship between the sine and osine funtions a. Tabular Copy and omplete the table using the triangles shown above Triangle Trigonometri Ratios sin 2 os 2 sin 2 + os 2 = ABC JKL XYZ sin A = os A = sin 2 A = os 2 A = sin C = os C = sin 2 C = os 2 C = sin J = os J = sin 2 J = os 2 J = sin L = os L = sin 2 L = os 2 L = sin X = os X = sin 2 X = os 2 X = sin Z = os Z = sin 2 Z = os 2 Z = b. Verbal Make a onjeture about the sum of the squares of the sine and osine funtions of an aute angle in a right triangle. H.O.T. Problems Use Higher-Order Thinking Skills 1. CHALLENGE Find a and in the triangle shown. 2. REASONING Use the definitions of the sine and osine ratios to define the tangent ratio. 64 Lesson 10-8 Trigonometri Ratios + (6a - ) (12a + ) - 2. OPEN ENDED Write a problem that uses the osine ratio to find the measure of an unknown angle in a triangle. Then solve the problem. 4. REASONING The sine and osine of an aute angle in a right triangle are equal. What an you onlude about the triangle?. WRITING IN MATH Explain how to use trigonometri ratios to find the missing length of a side of a right triangle given the measure of one aute angle and the length of one side.
8 Virginia SOL Pratie A.., G.8 6. Whih graph below represents the solution set for -2 x 4? A B C D PROBABILITY Suppose one hip is hosen from a bin with the hips shown. To the nearest tenth, what is the probability that a green hip is hosen? Color Number yellow blue 9 orange green red 6 F 0.2 H 0.6 G 0. J In the graph, for what value(s) of x is y = 0? A 0 C 1 B -1 D 1 and EXTENDED RESPONSE A 16-foot ladder is plaed against the side of a house so that the bottom of the ladder is 8 feet from the base of the house. a. If the bottom of the ladder is moved loser to the base of the house, does the height reahed by the ladder inrease or derease? b. What onlusion an you make about the distane between the bottom of the ladder and the base of the house and the height reahed by the ladder?. How high does the ladder reah if the ladder is feet from the base of the house? y x Spiral Review For eah set of measures given, find the measures of the missing sides if ABC DFH. (Lesson 10-) 60. a = 16, b = 12, = 8, f = 6 a h d 61. d = 9, f = 6, h = 4, b = a = 6, b = 21, h = 11, f = 14 b f 6. = 22., b = 20, h = 9, d = 2 Find the oordinates of the midpoint of the segment with the given endpoints. (Lesson 10-6) 64. (, ), (11, 9) 6. (8, 2), (6, 4) 66. (-1, ), (1, -) 6. FINANCIAL LITERACY A salesperson is paid $2,000 a year plus % of the amount in sales made. What is the amount of sales needed to have an annual inome greater than $4,000? (Lesson -) Skills Review Solve eah proportion. (Lesson 2-6) 68. _ 8 9 = _ 6 z 69. _ p 6 = 4_ 0. _ 0. r = _ _ = y_ 8.4 onneted.mgraw-hill.om 6
Chapter 7. Right Triangles and Trigonometry
hapter 7 Right Triangles and Trigonometry 7.1 pply the Pythagorean Theorem 7.2 Use the onverse of the Pythagorean Theorem 7.3 Use Similar Right Triangles 7.4 Special Right Triangles 7.5 pply the Tangent
More informationMATH STUDENT BOOK. 12th Grade Unit 6
MATH STUDENT BOOK 12th Grade Unit 6 Unit 6 TRIGONOMETRIC APPLICATIONS MATH 1206 TRIGONOMETRIC APPLICATIONS INTRODUCTION 3 1. TRIGONOMETRY OF OBLIQUE TRIANGLES 5 LAW OF SINES 5 AMBIGUITY AND AREA OF A TRIANGLE
More information7.1/7.2 Apply the Pythagorean Theorem and its Converse
7.1/7.2 Apply the Pythagorean Theorem and its Converse Remember what we know about a right triangle: In a right triangle, the square of the length of the is equal to the sum of the squares of the lengths
More informationBe sure to label all answers and leave answers in exact simplified form.
Pythagorean Theorem word problems Solve each of the following. Please draw a picture and use the Pythagorean Theorem to solve. Be sure to label all answers and leave answers in exact simplified form. 1.
More informationSolving Right Triangles. How do you solve right triangles?
Solving Right Triangles How do you solve right triangles? The Trigonometric Functions we will be looking at SINE COSINE TANGENT The Trigonometric Functions SINE COSINE TANGENT SINE Pronounced sign TANGENT
More informationWarm-Up Up Exercises. Use this diagram for Exercises If PR = 12 and m R = 19, find p. ANSWER If m P = 58 and r = 5, find p.
Warm-Up Up Exercises Use this diagram for Exercises 1 4. 1. If PR = 12 and m R = 19, find p. ANSWER 11.3 2. If m P = 58 and r = 5, find p. ANSWER 8.0 Warm-Up Up Exercises Use this diagram for Exercises
More information10-1. Three Trigonometric Functions. Vocabulary. Lesson
Chapter 10 Lesson 10-1 Three Trigonometric Functions BIG IDEA The sine, cosine, and tangent of an acute angle are each a ratio of particular sides of a right triangle with that acute angle. Vocabulary
More informationFinding Angles and Solving Right Triangles NEW SKILLS: WORKING WITH INVERSE TRIGONOMETRIC RATIOS. Calculate each angle to the nearest degree.
324 MathWorks 10 Workbook 7.5 Finding Angles and Solving Right Triangles NEW SKILLS: WORKING WITH INVERSE TRIGONOMETRIC RATIOS The trigonometric ratios discussed in this chapter are unaffected by the size
More informationIntroduction to Trigonometry
NAME COMMON CORE GEOMETRY- Unit 6 Introduction to Trigonometry DATE PAGE TOPIC HOMEWORK 1/22 2-4 Lesson 1 : Incredibly Useful Ratios Homework Worksheet 1/23 5-6 LESSON 2: Using Trigonometry to find missing
More informationAlgebra II. Slide 1 / 92. Slide 2 / 92. Slide 3 / 92. Trigonometry of the Triangle. Trig Functions
Slide 1 / 92 Algebra II Slide 2 / 92 Trigonometry of the Triangle 2015-04-21 www.njctl.org Trig Functions click on the topic to go to that section Slide 3 / 92 Trigonometry of the Right Triangle Inverse
More informationCh 8: Right Triangles and Trigonometry 8-1 The Pythagorean Theorem and Its Converse 8-2 Special Right Triangles 8-3 The Tangent Ratio
Ch 8: Right Triangles and Trigonometry 8-1 The Pythagorean Theorem and Its Converse 8- Special Right Triangles 8-3 The Tangent Ratio 8-1: The Pythagorean Theorem and Its Converse Focused Learning Target:
More informationChapter 3: Right Triangle Trigonometry
10C Name: Chapter 3: Right Triangle Trigonometry 3.1 The Tangent Ratio Outcome : Develop and apply the tangent ratio to solve problems that involve right triangles. Definitions: Adjacent side: the side
More informationName Class Date. Investigating a Ratio in a Right Triangle
Name lass Date Trigonometric Ratios Going Deeper Essential question: How do you find the tangent, sine, and cosine ratios for acute angles in a right triangle? In this chapter, you will be working etensively
More informationUnit 1 Trigonometry. Topics and Assignments. General Outcome: Develop spatial sense and proportional reasoning. Specific Outcomes:
1 Unit 1 Trigonometry General Outcome: Develop spatial sense and proportional reasoning. Specific Outcomes: 1.1 Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems
More informationObjectives: After completing this section, you should be able to do the following: Calculate the lengths of sides and angles of a right triangle using
Ch 13 - RIGHT TRIANGLE TRIGONOMETRY Objectives: After completing this section, you should be able to do the following: Calculate the lengths of sides and angles of a right triangle using trigonometric
More informationA lg e b ra II. Trig o n o m e try o f th e Tria n g le
1 A lg e b ra II Trig o n o m e try o f th e Tria n g le 2015-04-21 www.njctl.org 2 Trig Functions click on the topic to go to that section Trigonometry of the Right Triangle Inverse Trig Functions Problem
More informationG.8 Right Triangles STUDY GUIDE
G.8 Right Triangles STUDY GUIDE Name Date Block Chapter 7 Right Triangles Review and Study Guide Things to Know (use your notes, homework, quizzes, textbook as well as flashcards at quizlet.com (http://quizlet.com/4216735/geometry-chapter-7-right-triangles-flashcardsflash-cards/)).
More informationAW Math 10 UNIT 7 RIGHT ANGLE TRIANGLES
AW Math 10 UNIT 7 RIGHT ANGLE TRIANGLES Assignment Title Work to complete Complete 1 Triangles Labelling Triangles 2 Pythagorean Theorem 3 More Pythagorean Theorem Eploring Pythagorean Theorem Using Pythagorean
More informationDAY 1 - GEOMETRY FLASHBACK
DAY 1 - GEOMETRY FLASHBACK Sine Opposite Hypotenuse Cosine Adjacent Hypotenuse sin θ = opp. hyp. cos θ = adj. hyp. tan θ = opp. adj. Tangent Opposite Adjacent a 2 + b 2 = c 2 csc θ = hyp. opp. sec θ =
More informationName: Block: What I can do for this unit:
Unit 8: Trigonometry Student Tracking Sheet Math 10 Common Name: Block: What I can do for this unit: After Practice After Review How I Did 8-1 I can use and understand triangle similarity and the Pythagorean
More information14.1 Similar Triangles and the Tangent Ratio Per Date Trigonometric Ratios Investigate the relationship of the tangent ratio.
14.1 Similar Triangles and the Tangent Ratio Per Date Trigonometric Ratios Investigate the relationship of the tangent ratio. Using the space below, draw at least right triangles, each of which has one
More informationPractice For use with pages
9.1 For use with pages 453 457 Find the square roots of the number. 1. 36. 361 3. 79 4. 1089 5. 4900 6. 10,000 Approimate the square root to the nearest integer. 7. 39 8. 85 9. 105 10. 136 11. 17.4 1.
More informationName: Unit 8 Right Triangles and Trigonometry Unit 8 Similarity and Trigonometry. Date Target Assignment Done!
Unit 8 Similarity and Trigonometry Date Target Assignment Done! M 1-22 8.1a 8.1a Worksheet T 1-23 8.1b 8.1b Worksheet W 1-24 8.2a 8.2a Worksheet R 1-25 8.2b 8.2b Worksheet F 1-26 Quiz Quiz 8.1-8.2 M 1-29
More information2.1 The Tangent Ratio
2.1 The Tangent Ratio C 2.1 Concept: 14, 15 PreAP FPCM 10 (Ms. Carignan) Outcome FP10.4 Trigonometry Chapter 2 Page 1 PreAP FPCM 10 (Ms. Carignan) Outcome FP10.4 Trigonometry Chapter 2 Page 2 Online Video
More informationUNIT 9 - RIGHT TRIANGLES AND TRIG FUNCTIONS
UNIT 9 - RIGHT TRIANGLES AND TRIG FUNCTIONS Converse of the Pythagorean Theorem Objectives: SWBAT use the converse of the Pythagorean Theorem to solve problems. SWBAT use side lengths to classify triangles
More informationGeometry- Unit 6 Notes. Simplifying Radicals
Geometry- Unit 6 Notes Name: Review: Evaluate the following WITHOUT a calculator. a) 2 2 b) 3 2 c) 4 2 d) 5 2 e) 6 2 f) 7 2 g) 8 2 h) 9 2 i) 10 2 j) 2 2 k) ( 2) 2 l) 2 0 Simplifying Radicals n r Example
More informationSine (sin) = opposite hypotenuse
? Sine (sin) =? Sine (sin) = opposite hypotenuse ? Cosine (cos) =? Cosine (cos) = adjacent hypotenuse ? Tangent (tan) =? Tangent (tan) = opposite adjacent sin D=?? sin D = AB AD cos D=?? cos D = DB AD
More informationName Class Date. Essential question: How do you find the tangent, sine, and cosine ratios for acute angles in a right triangle?
Name lass Date 8-2 Trigonometric Ratios Going Deeper Essential question: How do you find the tangent, sine, and cosine ratios for acute angles in a right triangle? In this chapter, you will be working
More informationAWM 11 UNIT 4 TRIGONOMETRY OF RIGHT TRIANGLES
AWM 11 UNIT 4 TRIGONOMETRY OF RIGHT TRIANGLES Assignment Title Work to complete Complete 1 Triangles Labelling Triangles 2 Pythagorean Theorem Exploring Pythagorean Theorem 3 More Pythagorean Theorem Using
More informationA trigonometric ratio is a,
ALGEBRA II Chapter 13 Notes The word trigonometry is derived from the ancient Greek language and means measurement of triangles. Section 13.1 Right-Triangle Trigonometry Objectives: 1. Find the trigonometric
More informationAssignment. Pg. 567 #16-33, even pg 577 # 1-17 odd, 32-37
Assignment Intro to Ch. 8 8.1 8. Da 1 8. Da 8. Da 1 8. Da Review Quiz 8. Da 1 8. Da 8. Etra Practice 8.5 8.5 In-class project 8.6 Da 1 8.6 Da Ch. 8 review Worksheet Worksheet Worksheet Worksheet Worksheet
More informationReview of Sine, Cosine, and Tangent for Right Triangle
Review of Sine, Cosine, and Tangent for Right Triangle In trigonometry problems, all vertices (corners or angles) of the triangle are labeled with capital letters. The right angle is usually labeled C.
More informationUNIT 5 TRIGONOMETRY Lesson 5.4: Calculating Sine, Cosine, and Tangent. Instruction. Guided Practice 5.4. Example 1
Lesson : Calculating Sine, Cosine, and Tangent Guided Practice Example 1 Leo is building a concrete pathway 150 feet long across a rectangular courtyard, as shown in the following figure. What is the length
More information8.4 Special Right Triangles
8.4. Special Right Triangles www.ck1.org 8.4 Special Right Triangles Learning Objectives Identify and use the ratios involved with isosceles right triangles. Identify and use the ratios involved with 30-60-90
More informationChapter 8: Right Triangle Trigonometry
Haberman MTH 11 Setion I: The Trigonometri Funtions Chapter 8: Right Triangle Trigonometry As we studied in Part 1 of Chapter 3, if we put the same angle in the enter of two irles of different radii, we
More informationLesson Title 2: Problem TK Solving with Trigonometric Ratios
Part UNIT RIGHT solving TRIANGLE equations TRIGONOMETRY and inequalities Lesson Title : Problem TK Solving with Trigonometric Ratios Georgia Performance Standards MMG: Students will define and apply sine,
More informationSolv S ing olv ing ight ight riang les iangles 8-3 Solving Right Triangles Warm Up Use ABC for Exercises If a = 8 and b = 5, find c
Warm Up Lesson Presentation Lesson Quiz Warm Up Use ABC for Exercises 1 3. 1. If a = 8 and b = 5, find c. 2. If a = 60 and c = 61, find b. 11 3. If b = 6 and c = 10, find sin B. 0.6 Find AB. 4. A(8, 10),
More informationCongruence and Similarity in Triangles Pg. 378 # 1, 4 8, 12. Solving Similar Triangle Problems Pg. 386 # 2-12
UNIT 7 SIMILAR TRIANGLES AND TRIGONOMETRY Date Lesson TOPIC Homework May 4 7.1 7.1 May 8 7.2 7.2 Congruence and Similarity in Triangles Pg. 378 # 1, 4 8, 12 Solving Similar Triangle Problems Pg. 386 #
More informationMBF 3C. Foundations for College Mathematics Grade 11 College Mitchell District High School. Unit 1 Trigonometry 9 Video Lessons
MBF 3C Foundations for College Mathematics Grade 11 College Mitchell District High School Unit 1 Trigonometry 9 Video Lessons Allow no more than 15 class days for this unit This includes time for review
More information(13) Page #1 8, 12, 13, 15, 16, Even, 29 32, 39 44
Geometry/Trigonometry Unit 7: Right Triangle Notes Name: Date: Period: # (1) Page 430 #1 15 (2) Page 430 431 #16 23, 25 27, 29 and 31 (3) Page 437 438 #1 8, 9 19 odd (4) Page 437 439 #10 20 Even, 23, and
More informationAssignment Guide: Chapter 8 Geometry (L3)
Assignment Guide: Chapter 8 Geometry (L3) (91) 8.1 The Pythagorean Theorem and Its Converse Page 495-497 #7-31 odd, 37-47 odd (92) 8.2 Special Right Triangles Page 503-504 #7-12, 15-20, 23-28 (93) 8.2
More informationMath-2 Lesson 8-7: Unit 5 Review (Part -2)
Math- Lesson 8-7: Unit 5 Review (Part -) Trigonometric Functions sin cos A A SOH-CAH-TOA Some old horse caught another horse taking oats away. opposite ( length ) o sin A hypotenuse ( length ) h SOH adjacent
More information2) In a right triangle, with acute angle θ, sin θ = 7/9. What is the value of tan θ?
CC Geometry H Aim #26: Students rewrite the Pythagorean theorem in terms of sine and cosine ratios and write tangent as an identity in terms of sine and cosine. Do Now: 1) In a right triangle, with acute
More informationCumulative Review: SOHCAHTOA and Angles of Elevation and Depression
Cumulative Review: SOHCAHTOA and Angles of Elevation and Depression Part 1: Model Problems The purpose of this worksheet is to provide students the opportunity to review the following topics in right triangle
More informationMath 2201 Unit 3: Acute Triangle Trigonometry. Ch. 3 Notes
Rea Learning Goals, p. 17 text. Math 01 Unit 3: ute Triangle Trigonometry h. 3 Notes 3.1 Exploring Sie-ngle Relationships in ute Triangles (0.5 lass) Rea Goal p. 130 text. Outomes: 1. Define an aute triangle.
More informationStudent Instruction Sheet: Unit 4, Lesson 2. Ratios of Sides of Right-Angle Triangles
Student Instruction Sheet: Unit 4, Lesson 2 Ratios of Sides of Right-Angle s Suggested Time: 75 minutes What s important in this lesson: In this lesson, you will learn through investigation, the relationship
More information5B.4 ~ Calculating Sine, Cosine, Tangent, Cosecant, Secant and Cotangent WB: Pgs :1-10 Pgs : 1-7
SECONDARY 2 HONORS ~ UNIT 5B (Similarity, Right Triangle Trigonometry, and Proof) Assignments from your Student Workbook are labeled WB Those from your hardbound Student Resource Book are labeled RB. Do
More informationCK-12 Geometry: Inverse Trigonometric Ratios
CK-12 Geometry: Inverse Trigonometric Ratios Learning Objectives Use the inverse trigonometric ratios to find an angle in a right triangle. Solve a right triangle. Apply inverse trigonometric ratios to
More informationSOH CAH TOA Worksheet Name. Find the following ratios using the given right triangles
Name: Algebra II Period: 9.1 Introduction to Trig 12.1 Worksheet Name GETTIN' TRIGGY WIT IT SOH CAH TOA Find the following ratios using the given right triangles. 1. 2. Sin A = Sin B = Sin A = Sin B =
More informationReview (Law of sines and cosine) cosines)
Date:03/7,8/01 Review 6.1-6. Objetive: Apply the onept to use the law of the sines and osines to solve oblique triangles Apply the onept to find areas using the law of sines and osines Agenda: Bell ringer
More informationUnit 6: Triangle Geometry
Unit 6: Triangle Geometry Student Tracking Sheet Math 9 Principles Name: lock: What I can do for this unit: fter Practice fter Review How I id 6-1 I can recognize similar triangles using the ngle Test,
More informationabout touching on a topic and then veering off to talk about something completely unrelated.
The Tangent Ratio Tangent Ratio, Cotangent Ratio, and Inverse Tangent 8.2 Learning Goals In this lesson, you will: Use the tangent ratio in a right triangle to solve for unknown side lengths. Use the cotangent
More informationSM 2. Date: Section: Objective: The Pythagorean Theorem: In a triangle, or
SM 2 Date: Section: Objective: The Pythagorean Theorem: In a triangle, or. It doesn t matter which leg is a and which leg is b. The hypotenuse is the side across from the right angle. To find the length
More informationYou ll use the six trigonometric functions of an angle to do this. In some cases, you will be able to use properties of the = 46
Math 1330 Section 6.2 Section 7.1: Right-Triangle Applications In this section, we ll solve right triangles. In some problems you will be asked to find one or two specific pieces of information, but often
More informationInvestigating a Ratio in a Right Triangle. Leg opposite. Leg adjacent to A
Name lass ate 13.1 Tangent atio Essential uestion: How do you find the tangent ratio for an acute angle? esource Locker Explore Investigating a atio in a ight Triangle In a given a right triangle,, with
More informationName: Class: Date: Chapter 3 - Foundations 7. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Class: Date: Chapter 3 - Foundations 7 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the value of tan 59, to four decimal places. a.
More informationHistorical Note Trigonometry Ratios via Similarity
Section 12-6 Trigonometry Ratios via Similarity 1 12-6 Trigonometry Ratios via Similarity h 40 190 ft of elevation Figure 12-83 Measurements of buildings, structures, and some other objects are frequently
More informationUnit 6 Introduction to Trigonometry
Lesson 1: Incredibly Useful Ratios Opening Exercise Unit 6 Introduction to Trigonometry Use right triangle ΔABC to answer 1 3. 1. Name the side of the triangle opposite A in two different ways. 2. Name
More informationApply the Tangent Ratio. You used congruent or similar triangles for indirect measurement. You will use the tangent ratio for indirect measurement.
7.5 pply the Tangent Ratio efore Now You used congruent or similar triangles for indirect measurement. You will use the tangent ratio for indirect measurement. Why? So you can find the height of a roller
More informationSection 10.6 Right Triangle Trigonometry
153 Section 10.6 Right Triangle Trigonometry Objective #1: Understanding djacent, Hypotenuse, and Opposite sides of an acute angle in a right triangle. In a right triangle, the otenuse is always the longest
More informationRight Triangle Trigonometry
Right Triangle Trigonometry 1 The six trigonometric functions of a right triangle, with an acute angle, are defined by ratios of two sides of the triangle. hyp opp The sides of the right triangle are:
More informationMath-3 Lesson 6-1. Trigonometric Ratios for Right Triangles and Extending to Obtuse angles.
Math-3 Lesson 6-1 Trigonometric Ratios for Right Triangles and Extending to Obtuse angles. Right Triangle: has one angle whose measure is. 90 The short sides of the triangle are called legs. The side osite
More informationMath 1201 Chapter 2 Review
ath 1201 hapter 2 Review ultiple hoice Identify the choice that best completes the statement or answers the question. 1. etermine tan and tan. 8 10 a. tan = 1.25; tan = 0.8 c. tan = 0.8; tan = 1.25 b.
More informationarchitecture, physics... you name it, they probably use it.
The Cosine Ratio Cosine Ratio, Secant Ratio, and Inverse Cosine.4 Learning Goals In this lesson, you will: Use the cosine ratio in a right triangle to solve for unknown side lengths. Use the secant ratio
More informationAngles of a Triangle. Activity: Show proof that the sum of the angles of a triangle add up to Finding the third angle of a triangle
Angles of a Triangle Activity: Show proof that the sum of the angles of a triangle add up to 180 0 Finding the third angle of a triangle Pythagorean Theorem Is defined as the square of the length of the
More informationLesson 2: Right Triangle Trigonometry
Lesson : Right Triangle Trigonometry lthough Trigonometry is used to solve many prolems, historially it was first applied to prolems that involve a right triangle. This an e extended to non-right triangles
More informationSemester Exam Review. Honors Geometry A
Honors Geometry 2015-2016 The following formulas will be provided in the student examination booklet. Pythagorean Theorem In right triangle with right angle at point : 2 2 2 a b c b c a Trigonometry In
More informationBe sure to label all answers and leave answers in exact simplified form.
Pythagorean Theorem word problems Solve each of the following. Please draw a picture and use the Pythagorean Theorem to solve. Be sure to label all answers and leave answers in exact simplified form. 1.
More informationInequalities in Triangles Geometry 5-5
Inequalities in Triangles Geometry 5-5 Name: ate: Period: Theorem 5-10 Theorem 5-11 If two sides of a triangle are not If two angles of a triangle are not congruent, then the larger angle congruent, then
More information13.2 Sine and Cosine Ratios
Name lass Date 13.2 Sine and osine Ratios Essential Question: How can you use the sine and cosine ratios, and their inverses, in calculations involving right triangles? Explore G.9. Determine the lengths
More informationThree Angle Measure. Introduction to Trigonometry. LESSON 9.1 Assignment
LESSON.1 Assignment Name Date Three Angle Measure Introduction to Trigonometry 1. Analyze triangle A and triangle DEF. Use /A and /D as the reference angles. E 7.0 cm 10.5 cm A 35 10.0 cm D 35 15.0 cm
More informationTrigonometry is concerned with the connection between the sides and angles in any right angled triangle.
Trigonometry Obj: I can to use trigonometry to find unknown sides and unknown angles in a triangle. Trigonometry is concerned with the connection between the sides and angles in any right angled triangle.
More informationMR. JIMENEZ FINAL EXAM REVIEW GEOMETRY 2011
PAGE 1 1. The area of a circle is 25.5 in. 2. Find the circumference of the circle. Round your answers to the nearest tenth. 2. The circumference of a circle is 13.1 in. Find the area of the circle. Round
More information2.0 Trigonometry Review Date: Pythagorean Theorem: where c is always the.
2.0 Trigonometry Review Date: Key Ideas: The three angles in a triangle sum to. Pythagorean Theorem: where c is always the. In trigonometry problems, all vertices (corners or angles) of the triangle are
More informationSkills Practice Skills Practice for Lesson 7.1
Skills Practice Skills Practice for Lesson.1 Name Date Tangent Ratio Tangent Ratio, Cotangent Ratio, and Inverse Tangent Vocabulary Match each description to its corresponding term for triangle EFG. F
More information9.1 Use Trigonometry with Right Triangles
9.1 Use Trigonometry with Right Triangles Use the Pythagorean Theorem to find missing lengths in right triangles. Find trigonometric ratios using right triangles. Use trigonometric ratios to find angle
More informationGeo, Chap 8 Practice Test, EV Ver 1
Name: Class: Date: ID: A Geo, Chap 8 Practice Test, EV Ver 1 Short Answer Find the length of the missing side. Leave your answer in simplest radical form. 1. (8-1) 2. (8-1) A grid shows the positions of
More informationYou ll use the six trigonometric functions of an angle to do this. In some cases, you will be able to use properties of the = 46
Math 1330 Section 6.2 Section 7.1: Right-Triangle Applications In this section, we ll solve right triangles. In some problems you will be asked to find one or two specific pieces of information, but often
More informationLesson 1: Slope and Distance
Common Core Georgia Performance Standards MCC8.G.8* (Transition Standard 01 013; asterisks denote Transition Standards) MCC9 1.G.GPE.4 MCC9 1.G.GPE.5 Essential Questions 1. How is the Pythagorean Theorem
More informationDAY 1 - Pythagorean Theorem
1 U n i t 6 10P Date: Name: DAY 1 - Pythagorean Theorem 1. 2. 3. 1 2 U n i t 6 10P Date: Name: 4. 5. 6. 7. 2 3 U n i t 6 10P Date: Name: IF there s time Investigation: Complete the table below using the
More informationChapter 7: Right Triangles and Trigonometry Name: Study Guide Block: Section and Objectives
Page 1 of 22 hapter 7: Right Triangles and Trigonometr Name: Stud Guide lock: 1 2 3 4 5 6 7 8 SOL G.8 The student will solve real-world problems involving right triangles b using the Pthagorean Theorem
More informationName: Pythagorean Theorem February 3, 2014
1. John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school? 5. A 26 foot long ladder is leaning up against a house with its base 10 feet away from
More informationTrigonometry Ratios. For each of the right triangles below, the labelled angle is equal to 40. Why then are these triangles similar to each other?
Name: Trigonometry Ratios A) An Activity with Similar Triangles Date: For each of the right triangles below, the labelled angle is equal to 40. Why then are these triangles similar to each other? Page
More informationAssignment. Framing a Picture Similar and Congruent Polygons
Assignment Assignment for Lesson.1 Name Date Framing a Picture Similar and Congruent Polygons Determine whether each pair of polygons is similar. If necessary, write the similarity statement. Determine
More informationUnit 8 Similarity and Trigonometry
Unit 8 Similarity and Trigonometry Target 8.1: Prove and apply properties of similarity in triangles using AA~, SSS~, SAS~ 8.1a Prove Triangles Similar by AA ~, SSS~, SAS~ 8.1b Use Proportionality Theorems
More informationThis simple one is based on looking at various sized right angled triangles with angles 37 (36á9 ), 53 (53á1 ) and 90.
TRIGONOMETRY IN A RIGHT ANGLED TRIANGLE There are various ways of introducing Trigonometry, including the use of computers, videos and graphics calculators. This simple one is based on looking at various
More informationUNIT 2 RIGHT TRIANGLE TRIGONOMETRY Lesson 1: Exploring Trigonometric Ratios Instruction
Prerequisite Skills This lesson requires the use of the following skills: measuring angles with a protractor understanding how to label angles and sides in triangles converting fractions into decimals
More informationGeometry. Chapter 7 Right Triangles and Trigonometry. Name Period
Geometry Chapter 7 Right Triangles and Trigonometry Name Period 1 Chapter 7 Right Triangles and Trigonometry ***In order to get full credit for your assignments they must me done on time and you must SHOW
More informationTheorem 8-1-1: The three altitudes in a right triangle will create three similar triangles
G.T. 7: state and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle. Understand and use the geometric mean to solve for missing parts of triangles. 8-1
More informationPythagorean Theorem Distance and Midpoints
Slide 1 / 78 Pythagorean Theorem Distance and Midpoints Slide 2 / 78 Table of Contents Pythagorean Theorem Distance Formula Midpoints Click on a topic to go to that section Slide 3 / 78 Slide 4 / 78 Pythagorean
More informationRight Triangle Trigonometry Definitions (Instructor Notes)
Right Triangle Trigonometry Definitions (Instructor Notes) This activity is designed for a 50 min. class. Materials: Triangles Print out the last 10 pages of this document. It helps to use different colors
More informationMath 144 Activity #2 Right Triangle Trig and the Unit Circle
1 p 1 Right Triangle Trigonometry Math 1 Activity #2 Right Triangle Trig and the Unit Circle We use right triangles to study trigonometry. In right triangles, we have found many relationships between the
More informationTriangle LMN and triangle OPN are similar triangles. Find the angle measurements for x, y, and z.
1 Use measurements of the two triangles elow to find x and y. Are the triangles similar or ongruent? Explain. 1a Triangle LMN and triangle OPN are similar triangles. Find the angle measurements for x,
More informationTriangles. Learning Objectives. Pre-Activity
Setion 3.2 Pre-tivity Preparation Triangles Geena needs to make sure that the dek she is building is perfetly square to the brae holding the dek in plae. How an she use geometry to ensure that the boards
More information5.5 Right Triangles. 1. For an acute angle A in right triangle ABC, the trigonometric functions are as follow:
5.5 Right Triangles 1. For an acute angle A in right triangle ABC, the trigonometric functions are as follow: sin A = side opposite hypotenuse cos A = side adjacent hypotenuse B tan A = side opposite side
More informationStudy Guide and Review - Chapter 10
State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence. 1. A triangle with sides having measures of 3, 4, and 6 is a
More informationStudy Guide and Review - Chapter 10
State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence. 1. A triangle with sides having measures of 3, 4, and 6 is a
More informationG r a d e 1 0 I n t r o d u c t i o n t o A p p l i e d a n d P r e - C a l c u l u s M a t h e m a t i c s ( 2 0 S )
G r a d e 0 I n t r o d u c t i o n t o A p p l i e d a n d P r e - C a l c u l u s M a t h e m a t i c s ( 0 S ) Midterm Practice Exam Answer Key G r a d e 0 I n t r o d u c t i o n t o A p p l i e d
More informationa. b. c. d. e. f. g. h.
Sec. Right Triangle Trigonometry Right Triangle Trigonometry Sides Find the requested unknown side of the following triangles. Name: a. b. c. d.? 44 8 5? 7? 44 9 58 0? e. f. g. h.?? 4 7 5? 38 44 6 49º?
More informationUnit O Student Success Sheet (SSS) Right Triangle Trigonometry (sections 4.3, 4.8)
Unit O Student Success Sheet (SSS) Right Triangle Trigonometry (sections 4.3, 4.8) Standards: Geom 19.0, Geom 20.0, Trig 7.0, Trig 8.0, Trig 12.0 Segerstrom High School -- Math Analysis Honors Name: Period:
More information