You 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

Size: px
Start display at page:

Download "You 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"

Transcription

1 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 you ll be asked to solve the triangle, which means that you will find all lengths and measures that were not given. You ll use the six trigonometric functions of an angle to do this. In some cases, you will be able to use properties of the triangles or of Example 1: Calculate x and y from the figure below. y x 100cm 30 o Example 2: In ABC with right angle C, A = 46 and AC = 12. Find BC. Round to the answer to the nearest hundredth. Example 3: Find x and y in the triangle below. 10 ft. y x 40 1

2 Math 1330 Section 6.2 Example 4: Draw a diagram to represent the given situation. Then find the indicated measures to the nearest degree. An isosceles triangle has sides measuring 20 inches, 54 inches and 54 inches. What are the measures of the angle? Angle of Elevation The angle of elevation is an angle that s formed by the horizontal ray and another ray above the horizontal. So when viewing an object at a point above the horizontal, the angle between the line of sight and horizontal is angle of elevation in the figure below. Example 5: Draw a diagram to represent the given situation. The find the indicate measure to the nearest tenth. The angle elevation to the top of a building from a point on the ground 125 feet away from the building is 8. How tall is the building? 2

3 Math 1330 Section 6.2 Example 6: Draw a diagram to represent the given situation. The find the indicate measure to the nearest tenth. A 16-foot ladder leans against a building. The ladder forms an angle of 70 with the ground. a) How high up the building does the ladder reach? b) What is the horizontal distance from the foot of the ladder to the base of the building? Angle of Depression The angle of depression is an angle that s formed by the horizontal ray and another ray below the horizontal. So when viewing an object at a point above the horizontal, the angle between the line of sight and horizontal is angle of elevation in the figure below. Example 7: Draw a diagram to represent the given situation. The find the indicate measure to the nearest tenth. Dave is at the top of a hill. He looks down and spots his car at a 61 angle of depression. If the hill is 59 meters high, how far is his car from the base of the hill? 3

4 Math 1330 Section 6.2 Example 8: Mike stands 450 feet from the base of the Empire State Building and sights the top of the building. If the Empire State Building is 1,453 feet tall, approximate the angle of elevation from Mike s perspective as he sights the top of the building. (Disregard Mike s height in your calculations.) 4

5 Math 1330 Section Area of a Triangle In this section, we ll use a familiar formula and a new formula to find the area of a triangle. Given a Recall the area of a triangle is given by 1 A = bh. We normally used this formula when we knew 2 the height of the triangle. However if the height is not given we must solve for it some way. So we solve for the height of the triangle by breaking the given triangle down into right triangles and use our trigonometric function (sine) to solve for the height. Area of a Trangle b 1 A = ab sinθ 2 a, b are the lengths of two sides of a triangle θ is the angle between them. Example 1: Find the exact area of the triangle

6 Math 1330 Section 7.2 Example 2: Find the exact area of the triangle Example 3: Find the area of an isosceles triangle with legs measuring 12 inches and the base angle is 30 degrees each. Example 4: If the area of angle F. EFG is 30 in 2, e = 8 in. and g = 15 in, find all possible measures of

7 Math 1330 Section 7.2 Example 5: A regular hexagon is inscribed in a circle of radius 6m. Find the area of the hexagon. Area of a Segment of a Circle You can also find the area of a segment of a circle. The shaded area of the picture is an example of a segment of a circle. B O A To find the area of a segment, find the area of the sector with central angle θ and radius OA. Then find the area of OAB. Then subtract the area of the triangle from the area of the sector. Area of a sector of a circle = Area of the segment = Area 1 r 2 θ 2 Area sec tor Example 6: Find the area of the segment of the circle with radius 6 meters and central angle 3π measuring. 4 triangle

8 Math 1330 Section 7.3 Section 7.3: Law of Sines and Law of Cosines Sometimes you will need to solve a triangle that is not a right triangle. This type of triangle is called an oblique triangle. To solve an oblique triangle you will not be able to use right triangle trigonometry. Instead, you will use the Law of Sines and/or the Law of Cosines. You will typically be given three parts of the triangle and you will be asked to find the other three. The approach you will take to the problem will depend on the information that is given. If you are given SSS (the lengths of all three sides) or SAS (the lengths of two sides and the measure of the included angle), you will use the Law of Cosines to solve the triangle. If you are given SAA (the measures of two angles and one side) or SSA (the measures of two sides and the measure of an angle that is not the included angle), you will use the Law of Sines to solve the triangle. Recall from your geometry course that SSA does not necessarily determine a triangle. We will need to take special care when this is the given information. Here s the Law of Cosines. In any triangle ABC, = + 2cos = + 2cos = + 2cos The development of one case of this formula is given in detail in the online text. Here s the Law of Sines. In any triangle ABC, sin =sin =sin The development of this formula is given in detail in the online text. Here are some facts about solving triangles that may be helpful in this section. If you are given SSS, SAS or SAA, the information determines a unique triangle. If you are given SSA, the information given may determine 0, 1 or 2 triangles. If this is the information you are given, you will have some additional work to do. Since you will have three pieces of information to find when solving a triangle, it is possible for you to use both the Law of Sines and the Law of Cosines in the same problem. When drawing a triangle, the measure of the largest angle is opposite the longest side; the measure of the middle-sized angle is opposite the middle-sized side; and the measure of the smallest angle is opposite the shortest side. Suppose a, b and c are suggested to be the lengths of the three sides of a triangle. Suppose that c is the biggest of the three measures. In order for a, b and c to form a triangle, this inequality must be true: a + b > c. So, the sum of the two smaller sides must be greater than the third side. 1

You 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

You 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 information

Section The Law of Sines and the Law of Cosines

Section The Law of Sines and the Law of Cosines Section 7.3 - The Law of Sines and the Law of Cosines Sometimes you will need to solve a triangle that is not a right triangle. This type of triangle is called an oblique triangle. To solve an oblique

More information

UNIT 9 - RIGHT TRIANGLES AND TRIG FUNCTIONS

UNIT 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 information

5.5 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: 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 information

Right Triangle Trigonometry

Right 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 information

Introduction to Trigonometry

Introduction 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 information

7.1/7.2 Apply the Pythagorean Theorem and its Converse

7.1/7.2 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 information

Packet Unit 5 Trigonometry Honors Math 2 17

Packet Unit 5 Trigonometry Honors Math 2 17 Packet Unit 5 Trigonometry Honors Math 2 17 Homework Day 12 Part 1 Cumulative Review of this unit Show ALL work for the following problems! Use separate paper, if needed. 1) If AC = 34, AB = 16, find sin

More information

Name: Unit 8 Right Triangles and Trigonometry Unit 8 Similarity and Trigonometry. Date Target Assignment Done!

Name: 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 information

Packet Unit 5 Right Triangles Honors Common Core Math 2 1

Packet Unit 5 Right Triangles Honors Common Core Math 2 1 Packet Unit 5 Right Triangles Honors Common Core Math 2 1 Day 1 HW Find the value of each trigonometric ratio. Write the ratios for sinp, cosp, and tanp. Remember to simplify! 9. 10. 11. Packet Unit 5

More information

Preview: Correctly fill in the missing side lengths (a, b, c) or the missing angles (α, β, γ) on the following diagrams.

Preview: Correctly fill in the missing side lengths (a, b, c) or the missing angles (α, β, γ) on the following diagrams. Preview: Correctly fill in the missing side lengths (a, b, c) or the missing angles (α, β, γ) on the following diagrams. γ b a β c α Goal: In chapter 1 we were given information about a right triangle

More information

Cumulative Review: SOHCAHTOA and Angles of Elevation and Depression

Cumulative 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 information

Chapter Nine Notes SN P U1C9

Chapter Nine Notes SN P U1C9 Chapter Nine Notes SN P UC9 Name Period Section 9.: Applications Involving Right Triangles To evaluate trigonometric functions with a calculator, there are a few important things to know: On your calculator,

More information

G.8 Right Triangles STUDY GUIDE

G.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 information

Algebra II. Slide 1 / 92. Slide 2 / 92. Slide 3 / 92. Trigonometry of the Triangle. Trig Functions

Algebra 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 information

Solving Right Triangles. How do you solve right triangles?

Solving 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 information

A lg e b ra II. Trig o n o m e try o f th e Tria n g le

A 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 information

Trigonometric Ratios and Functions

Trigonometric Ratios and Functions Algebra 2/Trig Unit 8 Notes Packet Name: Date: Period: # Trigonometric Ratios and Functions (1) Worksheet (Pythagorean Theorem and Special Right Triangles) (2) Worksheet (Special Right Triangles) (3) Page

More information

Review of Sine, Cosine, and Tangent for Right Triangle

Review 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 information

Exercise 1. Exercise 2. MAT 012 SS218 Worksheet 9 Sections Name: Consider the triangle drawn below. C. c a. A b

Exercise 1. Exercise 2. MAT 012 SS218 Worksheet 9 Sections Name: Consider the triangle drawn below. C. c a. A b Consider the triangle drawn below. C Exercise 1 c a A b B 1. Suppose a = 5 and b = 12. Find c, and then find sin( A), cos( A), tan( A), sec( A), csc( A), and cot( A). 2. Now suppose a = 10 and b = 24.

More information

5B.4 ~ Calculating Sine, Cosine, Tangent, Cosecant, Secant and Cotangent WB: Pgs :1-10 Pgs : 1-7

5B.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 information

Unit 5 Day 5: Law of Sines and the Ambiguous Case

Unit 5 Day 5: Law of Sines and the Ambiguous Case Unit 5 Day 5: Law of Sines and the Ambiguous Case Warm Up: Day 5 Draw a picture and solve. Label the picture with numbers and words including the angle of elevation/depression and height/length. 1. The

More information

DAY 1 - GEOMETRY FLASHBACK

DAY 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 information

A. 180 B. 108 C. 360 D. 540

A. 180 B. 108 C. 360 D. 540 Part I - Multiple Choice - Circle your answer: REVIEW FOR FINAL EXAM - GEOMETRY 2 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C.

More information

Geometry- Unit 6 Notes. Simplifying Radicals

Geometry- 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 information

AWM 11 UNIT 4 TRIGONOMETRY OF RIGHT TRIANGLES

AWM 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 information

Unit 7: Trigonometry Part 1

Unit 7: Trigonometry Part 1 100 Unit 7: Trigonometry Part 1 Right Triangle Trigonometry Hypotenuse a) Sine sin( α ) = d) Cosecant csc( α ) = α Adjacent Opposite b) Cosine cos( α ) = e) Secant sec( α ) = c) Tangent f) Cotangent tan(

More information

AW Math 10 UNIT 7 RIGHT ANGLE TRIANGLES

AW 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 information

Youngstown State University Trigonometry Final Exam Review (Math 1511)

Youngstown State University Trigonometry Final Exam Review (Math 1511) Youngstown State University Trigonometry Final Exam Review (Math 1511) 1. Convert each angle measure to decimal degree form. (Round your answers to thousandths place). a) 75 54 30" b) 145 18". Convert

More information

Non-right Triangles: Law of Cosines *

Non-right Triangles: Law of Cosines * OpenStax-CNX module: m49405 1 Non-right Triangles: Law of Cosines * OpenStax This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 In this section, you will:

More information

Mathematics Placement Assessment

Mathematics Placement Assessment Mathematics Placement Assessment Courage, Humility, and Largeness of Heart Oldfields School Thank you for taking the time to complete this form accurately prior to returning this mathematics placement

More information

2.0 Trigonometry Review Date: Pythagorean Theorem: where c is always the.

2.0 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 information

: Find the values of the six trigonometric functions for θ. Special Right Triangles:

: Find the values of the six trigonometric functions for θ. Special Right Triangles: ALGEBRA 2 CHAPTER 13 NOTES Section 13-1 Right Triangle Trig Understand and use trigonometric relationships of acute angles in triangles. 12.F.TF.3 CC.9- Determine side lengths of right triangles by using

More information

10-1. Three Trigonometric Functions. Vocabulary. Lesson

10-1. 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 information

6. If QRSTU is a regular pentagon, what is the measure of T? 1. If STUV is a parallelogram, what are the coordinates of point U?

6. If QRSTU is a regular pentagon, what is the measure of T? 1. If STUV is a parallelogram, what are the coordinates of point U? 1. If UV is a parallelogram, what are the coordinates of point U?. If RU is a regular pentagon, what is the measure of? (0, y) U(?,?) (, 0) V( + z, 0) 7. hree siblings are to share an inheritance of $1,0

More information

CK-12 Geometry: Inverse Trigonometric Ratios

CK-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 information

SM 2. Date: Section: Objective: The Pythagorean Theorem: In a triangle, or

SM 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 information

MATH 1112 Trigonometry Final Exam Review

MATH 1112 Trigonometry Final Exam Review MATH 1112 Trigonometry Final Exam Review 1. Convert 105 to exact radian measure. 2. Convert 2 to radian measure to the nearest hundredth of a radian. 3. Find the length of the arc that subtends an central

More information

Math-2 Lesson 8-7: Unit 5 Review (Part -2)

Math-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 information

Geometry Final Exam - Study Guide

Geometry Final Exam - Study Guide Geometry Final Exam - Study Guide 1. Solve for x. True or False? (questions 2-5) 2. All rectangles are rhombuses. 3. If a quadrilateral is a kite, then it is a parallelogram. 4. If two parallel lines are

More information

These are the type of problems that you will be working on in class. These problems are from Lesson 7.

These are the type of problems that you will be working on in class. These problems are from Lesson 7. Pre-Class Problems 10 for Wednesda, October 10 These are the tpe of problems that ou will be working on in class. These problems are from Lesson 7. Solution to Problems on the Pre-Eam. You can go to the

More information

2/10/ The Law of Sines. Copyright Cengage Learning. All rights reserved. Objectives. The Law of Sines. The Ambiguous Case.

2/10/ The Law of Sines. Copyright Cengage Learning. All rights reserved. Objectives. The Law of Sines. The Ambiguous Case. 6.5 Copyright Cengage Learning. All rights reserved. Objectives 2 3 1 The trigonometric functions can also be used to solve oblique triangles, that is, triangles with no right angles. For instance, if

More information

Chapters 1-5 Secondary Math II Name SAGE Test Review WS Please remember to show all your work to receive full credit.

Chapters 1-5 Secondary Math II Name SAGE Test Review WS Please remember to show all your work to receive full credit. Chapters 1-5 Secondary Math II Name SAGE Test Review WS Period Please remember to show all your work to receive full credit. 1. Find the distance and the midpoint between (-4,-9) & (1,-8). No decimals!

More information

Warm Up: please factor completely

Warm Up: please factor completely Warm Up: please factor completely 1. 2. 3. 4. 5. 6. vocabulary KEY STANDARDS ADDRESSED: MA3A2. Students will use the circle to define the trigonometric functions. a. Define and understand angles measured

More information

Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them.

Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them. Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them. Chapter 9 and 10: Right Triangles and Trigonometric Ratios 1. The hypotenuse of a right

More information

2. A circle is inscribed in a square of diagonal length 12 inches. What is the area of the circle?

2. A circle is inscribed in a square of diagonal length 12 inches. What is the area of the circle? March 24, 2011 1. When a square is cut into two congruent rectangles, each has a perimeter of P feet. When the square is cut into three congruent rectangles, each has a perimeter of P 6 feet. Determine

More information

Unit 8 Similarity and Trigonometry

Unit 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 information

I. Model Problems II. Practice III. Challenge Problems IV. Answer Key. Sine, Cosine Tangent

I. Model Problems II. Practice III. Challenge Problems IV. Answer Key. Sine, Cosine Tangent On Twitter: twitter.com/engagingmath On FaceBook: www.mathworksheetsgo.com/facebook I. Model Problems II. Practice III. Challenge Problems IV. Answer Key Web Resources Sine, Cosine Tangent www.mathwarehouse.com/trigonometry/sine-cosine-tangent.html

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 1)

More information

4. Given Quadrilateral HIJG ~ Quadrilateral MNOL, find x and y. x =

4. Given Quadrilateral HIJG ~ Quadrilateral MNOL, find x and y. x = Name: DUE: HOUR: 2016 2017 Geometry Final Exam Review 1. Find x. Round to the nearest hundredth. x = 2. Find x. x = 3. Given STU ~ PQR, find x. x = 4. Given Quadrilateral HIJG ~ Quadrilateral MNOL, find

More information

Unit 7 - Similarity 2. The perimeter of a rectangle is 156 cm. The ratio of the length to the width is 9:4. Find the width of the rectangle.

Unit 7 - Similarity 2. The perimeter of a rectangle is 156 cm. The ratio of the length to the width is 9:4. Find the width of the rectangle. Geometry B Final Exam Review Spring 2015 Name: 1. The ratio of the measures of the angles of a triangle is 4:5:6. What is the smallest angle s measure? Unit 7 - Similarity 2. The perimeter of a rectangle

More information

While you wait: Without consulting any resources or asking your friends write down everthing you remember about the:

While you wait: Without consulting any resources or asking your friends write down everthing you remember about the: While you wait: Without consulting any resources or asking your friends write down everthing you remember about the: Copyright 2007 Pearson Education, Inc. Slide 10-1 Sec 9.3 The Law of Sines Oblique Triangles

More information

TRIGONOMETRY. Meaning. Dear Reader

TRIGONOMETRY. Meaning. Dear Reader TRIGONOMETRY Dear Reader In your previous classes you have read about triangles and trigonometric ratios. A triangle is a polygon formed by joining least number of points i.e., three non-collinear points.

More information

Review for Spring Final Exam Geometry 1. Classify the figure. Name the vertices, edges, and base.

Review for Spring Final Exam Geometry 1. Classify the figure. Name the vertices, edges, and base. Name lass ue date Review for Spring Final Exam Geometry 1. lassify the figure. Name the vertices, edges, and base. 4. raw all 6 orthographic views from the given object. ssume there are no hidden cubes.

More information

Chapter 6 Review. Extending Skills with Trigonometry. Check Your Understanding

Chapter 6 Review. Extending Skills with Trigonometry. Check Your Understanding hapter 6 Review Extending Skills with Trigonometry heck Your Understanding. Explain why the sine law holds true for obtuse angle triangles as well as acute angle triangles. 2. What dimensions of a triangle

More information

hypotenuse adjacent leg Preliminary Information: SOH CAH TOA is an acronym to represent the following three 28 m 28 m opposite leg 13 m

hypotenuse adjacent leg Preliminary Information: SOH CAH TOA is an acronym to represent the following three 28 m 28 m opposite leg 13 m On Twitter: twitter.com/engagingmath On FaceBook: www.mathworksheetsgo.com/facebook I. odel Problems II. Practice Problems III. Challenge Problems IV. Answer ey Web Resources Using the inverse sine, cosine,

More information

Angles 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 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 information

Assignment. Framing a Picture Similar and Congruent Polygons

Assignment. 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 information

Geometry Final Exam Study Guide

Geometry Final Exam Study Guide Geometry Final Exam Study Guide Short Answer 1. Find the geometric mean between each pair of numbers. 256 and 841 2. Find x. Determine whether ΔQRS is a right triangle for the given vertices. Explain.

More information

3.0 Trigonometry Review

3.0 Trigonometry Review 3.0 Trigonometry Review In trigonometry problems, all vertices (corners or angles) of the triangle are labeled with capital letters. The right angle is usually labeled C. Sides are usually labeled with

More information

Trigonometry Final Review Exercises

Trigonometry Final Review Exercises 1 The exam will last 2 hours and will be entirely short answer. Be sure to provide adequate written work to justify your answers in order to receive full credit. You will be provided with a basic trig

More information

Ch 7 & 8 Exam Review. Note: This is only a sample. Anything covered in class or homework may appear on the exam.

Ch 7 & 8 Exam Review. Note: This is only a sample. Anything covered in class or homework may appear on the exam. Ch 7 & 8 Exam Review Note: This is only a sample. Anything covered in class or homework may appear on the exam. Determine whether there is sufficient information for solving a triangle, with the given

More information

Year 10 Term 3 Homework

Year 10 Term 3 Homework Yimin Math Centre Year 10 Term 3 Homework Student Name: Grade: Date: Score: Table of contents 3 Year 10 Term 3 Week 3 Homework 1 3.1 Further trigonometry................................... 1 3.1.1 Trigonometric

More information

Section 10.6 Right Triangle Trigonometry

Section 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 information

Unit 5 Day 4: Law of Sines & Area of Triangles with Sines

Unit 5 Day 4: Law of Sines & Area of Triangles with Sines Unit 5 Day 4: Law of Sines & Area of Triangles with Sines Warm-up: Draw a picture and solve. Label the picture with numbers and words including the angle of elevation/depression and height/length. 1. A

More information

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

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 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 information

Be sure to label all answers and leave answers in exact simplified form.

Be 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 information

Geometry Spring Final Review #1, 2014

Geometry Spring Final Review #1, 2014 Class: Date: Geometry Spring Final Review #1, 2014 Short Answer 1. Find the measure of each interior angle of a regular 45-gon. 2. Find the measure of each exterior angle of a regular decagon. 3. The door

More information

Unit 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) 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

Objective: Manipulate trigonometric properties to verify, prove, and understand trigonmetric relationships.

Objective: Manipulate trigonometric properties to verify, prove, and understand trigonmetric relationships. Objective: Manipulate trigonometric properties to verify, prove, and understand trigonmetric relationships. Apr 21 4:09 AM Warm-up: Determine the exact value of the following (without a calculator): sin

More information

Chapter 7. Right Triangles and Trigonometry

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 information

Geometry Second Semester Final Exam Review

Geometry Second Semester Final Exam Review Name: Class: Date: ID: A Geometry Second Semester Final Exam Review 1. Find the length of the leg of this right triangle. Give an approximation to 3 decimal places. 2. Find the length of the leg of this

More information

Chapter 3: Right Triangle Trigonometry

Chapter 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 information

Chapter 15 Right Triangle Trigonometry

Chapter 15 Right Triangle Trigonometry Chapter 15 Right Triangle Trigonometry Sec. 1 Right Triangle Trigonometry The most difficult part of Trigonometry is spelling it. Once we get by that, the rest is a piece of cake. efore we start naming

More information

Distance in Coordinate Geometry

Distance in Coordinate Geometry Page 1 of 6 L E S S O N 9.5 We talk too much; we should talk less and draw more. Distance in Coordinate Geometry Viki is standing on the corner of Seventh Street and 8th Avenue, and her brother Scott is

More information

Geometry Second Semester Review

Geometry Second Semester Review Class: Date: Geometry Second Semester Review Short Answer 1. Identify the pairs of congruent angles and corresponding sides. 2. Determine whether the rectangles are similar. If so, write the similarity

More information

GEOMETRY SEMESTER 2 REVIEW PACKET 2016

GEOMETRY SEMESTER 2 REVIEW PACKET 2016 GEOMETRY SEMESTER 2 REVIEW PACKET 2016 Your Geometry Final Exam will take place on Friday, May 27 th, 2016. Below is the list of review problems that will be due in order to prepare you: Assignment # Due

More information

17-18 CP Geometry Final Exam REVIEW

17-18 CP Geometry Final Exam REVIEW 1 17-18 CP Geometry Final Exam REVIEW Identify the scale factor of each dilation. 1. 2. Dilate the following given each scale factor. Be sure to label the images properly. 1 3. Scale factor of 4 4. Scale

More information

2.1 The Tangent Ratio

2.1 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 information

Lesson #64 First Degree Trigonometric Equations

Lesson #64 First Degree Trigonometric Equations Lesson #64 First Degree Trigonometric Equations A2.A.68 Solve trigonometric equations for all values of the variable from 0 to 360 How is the acronym ASTC used in trigonometry? If I wanted to put the reference

More information

Name: Block: What I can do for this unit:

Name: 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 information

Unit 6 Introduction to Trigonometry

Unit 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 information

UNIT 5 TRIGONOMETRY Lesson 5.4: Calculating Sine, Cosine, and Tangent. Instruction. Guided Practice 5.4. Example 1

UNIT 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 information

Name: 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. 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 information

SOH CAH TOA Worksheet Name. Find the following ratios using the given right triangles

SOH 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 information

Solving an Oblique Triangle

Solving an Oblique Triangle Several methods exist to solve an oblique triangle, i.e., a triangle with no right angle. The appropriate method depends on the information available for the triangle. All methods require that the length

More information

LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON

LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON Trig/Math Anal Name No LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON HW NO. SECTIONS ASSIGNMENT DUE TT 1 1 Practice Set D TT 1 6 TT 1 7 TT TT 1 8 & Application Problems 1 9

More information

The Pythagorean Theorem: For a right triangle, the sum of the two leg lengths squared is equal to the length of the hypotenuse squared.

The Pythagorean Theorem: For a right triangle, the sum of the two leg lengths squared is equal to the length of the hypotenuse squared. Math 1 TOOLKITS TOOLKIT: Pythagorean Theorem & Its Converse The Pythagorean Theorem: For a right triangle, the sum of the two leg lengths squared is equal to the length of the hypotenuse squared. a 2 +

More information

Lesson 26 - Review of Right Triangle Trigonometry

Lesson 26 - Review of Right Triangle Trigonometry Lesson 26 - Review of Right Triangle Trigonometry PreCalculus Santowski PreCalculus - Santowski 1 (A) Review of Right Triangle Trig Trigonometry is the study and solution of Triangles. Solving a triangle

More information

Checkpoint 1 Define Trig Functions Solve each right triangle by finding all missing sides and angles, round to four decimal places

Checkpoint 1 Define Trig Functions Solve each right triangle by finding all missing sides and angles, round to four decimal places Checkpoint 1 Define Trig Functions Solve each right triangle by finding all missing sides and angles, round to four decimal places. 1.. B P 10 8 Q R A C. Find the measure of A and the length of side a..

More information

Find sin R and sin S. Then find cos R and cos S. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary.

Find sin R and sin S. Then find cos R and cos S. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary. Name Homework Packet 7.6 7.7 LESSON 7.6 For use with pages 473-480 AND LESSON 7.7 For use with pages 483 489 Find sin R and sin S. Then find cos R and cos S. Write each answer as a fraction and as a decimal.

More information

Lesson Title 2: Problem TK Solving with Trigonometric Ratios

Lesson 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 information

UNIT 4 MODULE 2: Geometry and Trigonometry

UNIT 4 MODULE 2: Geometry and Trigonometry Year 12 Further Mathematics UNIT 4 MODULE 2: Geometry and Trigonometry CHAPTER 8 - TRIGONOMETRY This module covers the application of geometric and trigonometric knowledge and techniques to various two-

More information

Assignment Guide: Chapter 8 Geometry (L3)

Assignment 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 information

Triangle Trigonometry

Triangle Trigonometry Honors Finite/Brief: Trigonometry review notes packet Triangle Trigonometry Right Triangles All triangles (including non-right triangles) Law of Sines: a b c sin A sin B sin C Law of Cosines: a b c bccos

More information

Now, we need to refresh our memory of some axioms from Geometry. 3 sides known

Now, we need to refresh our memory of some axioms from Geometry. 3 sides known 9.3 The Law of Sines First we need the definition for an oblique triangle. This is nothing but a triangle that is not a right triangle. In other words, all angles in the triangle are not of a measure of

More information

Geometry SIA #3. Name: Class: Date: Short Answer. 1. Find the perimeter of parallelogram ABCD with vertices A( 2, 2), B(4, 2), C( 6, 1), and D(0, 1).

Geometry SIA #3. Name: Class: Date: Short Answer. 1. Find the perimeter of parallelogram ABCD with vertices A( 2, 2), B(4, 2), C( 6, 1), and D(0, 1). Name: Class: Date: ID: A Geometry SIA #3 Short Answer 1. Find the perimeter of parallelogram ABCD with vertices A( 2, 2), B(4, 2), C( 6, 1), and D(0, 1). 2. If the perimeter of a square is 72 inches, what

More information

10.6 Area and Perimeter of Regular Polygons

10.6 Area and Perimeter of Regular Polygons 10.6. Area and Perimeter of Regular Polygons www.ck12.org 10.6 Area and Perimeter of Regular Polygons Learning Objectives Calculate the area and perimeter of a regular polygon. Review Queue 1. What is

More information

Day 4 Trig Applications HOMEWORK

Day 4 Trig Applications HOMEWORK Day 4 Trig Applications HOMEWORK 1. In ΔABC, a = 0, b = 1, and mc = 44º a) Find the length of side c to the nearest integer. b) Find the area of ΔABC to the nearest tenth.. In ΔABC, ma = 50º, a = 40, b

More information

Skills Practice Skills Practice for Lesson 7.1

Skills 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 information