Using the Quadrant. Protractor. Eye Piece. You can measure angles of incline from 0º ( horizontal ) to 90º (vertical ). Ignore measurements >90º.

Size: px
Start display at page:

Download "Using the Quadrant. Protractor. Eye Piece. You can measure angles of incline from 0º ( horizontal ) to 90º (vertical ). Ignore measurements >90º."

Transcription

1 Using the Quadrant Eye Piece Protractor Handle You can measure angles of incline from 0º ( horizontal ) to 90º (vertical ). Ignore measurements 90º. Plumb Bob ø <----Read angle of incline (ø) here. Eye ø

2 Using the Quadrant To Make a Similar Triangle. Use the quadrant to measure the height of tall objects in an indirect manner. First, locate yourself on a piece of ground that is level with the object to be measured. The object's base and your feet should be on the same horizontal plane. Measure the distance from your feet to the base of the object and record it on the diagram. Choose a multiple of ten feet (or other linear unit ) for this distance to simplify calculation. Second, walk to the object and mark it with a piece of marking tape at your eye level.. The quadrant should read 0º when you aim it at the eye level tape mark. Measure this height and record it on the diagram. Object to be measured Next, aim the quadrant at the top of the object to be measured. Aim the quadrant at the top of the object. - Have your partner read the quadrant's protractor as you hold it steady. The angle of incline should be between 0º and 90º. After that, record your angle of incline on the diagram. Finally, use these measurements to determine the object's height using the graph paper worksheet. Angle of incline: What is your eye level height? Sight a level line and mark the object at that height. Marking tape Make sure that you add your eye height to your height calculation. What is the distance to the object? Measure this distance accurately with a tape measure. < Level ground- - -

3 Using the Quadrant To Determine the Opposite Side Using Tangent. Use the quadrant to measure the height of tall objects in an indirect manner. First, locate yourself on a piece of ground that is level with the object to be measured. The object's base and your feet should be on the same horizontal plane. Measure the distance from your feet to the base of the object and record it on the diagram. Choose a multiple of ten feet (or other linear unit ) for this distance to simplify calculation. Second, walk to the object and mark it with a piece of marking tape at your eye level. Measure this height and record it on the diagram. Third, aim the quadrant at the object to be measured. The quadrant should read 0º when you aim it at the eye level tape mark. - Have your partner read the quadrant's protractor as you hold it steady. Aim the quadrant at the top of the object. Have your partner read the quadrant as you hold it steady. The angle of incline should be between 0º and 90º. Record your angle of incline on the diagram. Object to be measured Finally, Substitute measured values for variables on the following tangent worksheet.. Angle of incline: What is your eye level height? Sight a level line and mark the object at that height. Marking tape Make sure that you add your eye height to your height calculation. Measure this distance accurately with a tape measure. < Level ground- - -

4 Using the Quadrant To Find The Height of an Object Using the Tangent Function. Side opposite Ø Object ( Ø Use the Quadrant to find this angle(ø ). Measured side adjacent to Ø = What is Ø? What is Tan Ø? (Find this on your calculator, or from a Tangent table.) How long is the side adjacent Ø? The side opposite to Ø = "H" Tan Ø = So... Tan Ø ( Side Adjacent ) = Side Opposite Substitute measured values, then evaluate: ( ) = H

5 Make a similar triangle to measure indirectly. Using the Quadrant Mark the angle of incline on the protractor. Vertical scale = horizontal scale. 90º 80º 70º 60º 50º 40º 30º 20º 10º v For estimation purposes only.

6 Make a similar triangle to measure indirectly. Using the Quadrant Mark the angle of incline on the protractor. Mark the distance to the object on the horizontal scale. Draw a vertical line at that point. Connect the protractor's vertex mark "V" with the angle you marked, then extend this line to the vertical line you drew. This intersection marks the object's height from your eye level. Read this vertical distance from the scale on the right. 60 feet 50 feet 40 feet 30 feet 90º 80º 70º 60º 50º 40º 20 feet 30º 20º 10º 10 feet v For estimation purposes only. 30 feet 40 feet 50 feet 60 feet 70 feet 80 feet 90 feet 100 feet

7 Make a similar triangle to measure indirectly. Using the Quadrant Mark the angle of incline on the protractor. Mark the distance to the object on the horizontal scale. Draw a vertical line at that point. Connect the protractor's vertex mark "V" with the angle you marked, then extend this line to the vertical line you drew. This intersection marks the object's height from your eye level. Read this vertical distance from the scale on the right. 120 feet 100 feet 80 feet 60 feet 90º 80º 70º 60º 50º 40º 40 feet 30º 20º 10º 20 feet v For estimation purposes only. 60 feet 80 feet 100 feet 120 feet 140 feet 160 feet 180 feet 200 feet

You can solve a right triangle if you know either of the following: Two side lengths One side length and one acute angle measure

You can solve a right triangle if you know either of the following: Two side lengths One side length and one acute angle measure Solving a Right Triangle A trigonometric ratio is a ratio of the lengths of two sides of a right triangle. Every right triangle has one right angle, two acute angles, one hypotenuse, and two legs. To solve

More information

Similarity, Right Triangles, and Trigonometry

Similarity, Right Triangles, and Trigonometry Instruction Goal: To provide opportunities for students to develop concepts and skills related to trigonometric ratios for right triangles and angles of elevation and depression Common Core Standards Congruence

More information

Trigonometry (Chapters 4 5) Sample Test #1 First, a couple of things to help out:

Trigonometry (Chapters 4 5) Sample Test #1 First, a couple of things to help out: First, a couple of things to help out: Page 1 of 24 Use periodic properties of the trigonometric functions to find the exact value of the expression. 1. cos 2. sin cos sin 2cos 4sin 3. cot cot 2 cot Sin

More information

4-1 Right Triangle Trigonometry

4-1 Right Triangle Trigonometry Find the exact values of the six trigonometric functions of θ. 1. The length of the side opposite θ is 8 is 18., the length of the side adjacent to θ is 14, and the length of the hypotenuse 3. The length

More information

7.1 Apply the Pythagorean Theorem

7.1 Apply the Pythagorean Theorem 7.1 Apply the Pythagorean Theorem Obj.: Find side lengths in right triangles. Key Vocabulary Pythagorean triple - A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation

More information

4-1 Right Triangle Trigonometry

4-1 Right Triangle Trigonometry Find the exact values of the six trigonometric functions of θ. 3. The length of the side opposite θ is 9, the length of the side adjacent to θ is 4, and the length of the hypotenuse is. 7. The length of

More information

Geometry 1. Unit 3: Perpendicular and Parallel Lines

Geometry 1. Unit 3: Perpendicular and Parallel Lines Geometry 1 Unit 3: Perpendicular and Parallel Lines Geometry 1 Unit 3 3.1 Lines and Angles Lines and Angles Parallel Lines Parallel lines are lines that are coplanar and do not intersect. Some examples

More information

Mid-Chapter Quiz: Lessons 4-1 through 4-4

Mid-Chapter Quiz: Lessons 4-1 through 4-4 Find the exact values of the six trigonometric functions of θ. Find the value of x. Round to the nearest tenth if necessary. 1. The length of the side opposite is 24, the length of the side adjacent to

More information

The Primary Trigonometric Ratios Word Problems

The Primary Trigonometric Ratios Word Problems The Primary Trigonometric Ratios Word Problems. etermining the measures of the sides and angles of right triangles using the primary ratios When we want to measure the height of an inaccessible object

More information

Solution: 2. Sketch the graph of 2 given the vectors and shown below.

Solution: 2. Sketch the graph of 2 given the vectors and shown below. 7.4 Vectors, Operations, and the Dot Product Quantities such as area, volume, length, temperature, and speed have magnitude only and can be completely characterized by a single real number with a unit

More information

Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.

Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle. Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.

More information

The Inscribed Angle Alternate A Tangent Angle

The Inscribed Angle Alternate A Tangent Angle Student Outcomes Students use the inscribed angle theorem to prove other theorems in its family (different angle and arc configurations and an arc intercepted by an angle at least one of whose rays is

More information

Any two right triangles, with one other angle congruent, are similar by AA Similarity. This means that their side lengths are.

Any two right triangles, with one other angle congruent, are similar by AA Similarity. This means that their side lengths are. Lesson 1 Trigonometric Functions 1. I CAN state the trig ratios of a right triangle 2. I CAN explain why any right triangle yields the same trig values 3. I CAN explain the relationship of sine and cosine

More information

Inverse Trigonometric Functions

Inverse Trigonometric Functions Inverse Trigonometric Functions I. Four Facts About Functions and Their Inverse Functions:. A function must be one-to-one (an horizontal line intersects it at most once) in order to have an inverse function..

More information

Lines. We have learned that the graph of a linear equation. y = mx +b

Lines. We have learned that the graph of a linear equation. y = mx +b Section 0. Lines We have learne that the graph of a linear equation = m +b is a nonvertical line with slope m an -intercept (0, b). We can also look at the angle that such a line makes with the -ais. This

More information

4-1 Right Triangle Trigonometry

4-1 Right Triangle Trigonometry Find the measure of angle θ. Round to the nearest degree, if necessary. 31. Because the lengths of the sides opposite θ and the hypotenuse are given, the sine function can be used to find θ. 35. Because

More information

10-4 Angles of Elevation and Depression. Do Now Lesson Presentation Exit Ticket

10-4 Angles of Elevation and Depression. Do Now Lesson Presentation Exit Ticket Do Now Lesson Presentation Exit Ticket Do Now #15 1. Identify the pairs of alternate interior angles. 2 and 7; 3 and 6 2. Use your calculator to find tan 30 to the nearest hundredth. 0.58 3. Solve. Round

More information

MATH 10 COMMON TRIGONOMETRY CHAPTER 2. is always opposite side b.

MATH 10 COMMON TRIGONOMETRY CHAPTER 2. is always opposite side b. MATH 10 OMMON TRIGONOMETRY HAPTER 2 (11 Days) Day 1 Introduction to the Tangent Ratio Review: How to set up your triangles: Angles are always upper case ( A,, etc.) and sides are always lower case (a,b,c).

More information

Michael Svec Students will understand how images are formed in a flat mirror.

Michael Svec Students will understand how images are formed in a flat mirror. Unit Title Topic Name and email address of person submitting the unit Aims of unit Indicative content Resources needed Teacher notes Forming Images Physics Light and optics Michael Svec Michael.Svec@furman.edu

More information

Physics 202 Homework 8

Physics 202 Homework 8 Physics 202 Homework 8 May 22, 203. A beam of sunlight encounters a plate of crown glass at a 45.00 angle of 0.35 incidence. Using the data in Figure, find the angle between the violet ray and the red

More information

Biggar High School Mathematics Department. National 4 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department. National 4 Learning Intentions & Success Criteria: Assessing My Progress Biggar High School Mathematics Department National 4 Learning Intentions & Success Criteria: Assessing My Progress Expressions and Formulae Topic Learning Intention Success Criteria I understand this Algebra

More information

Trigonometry on Right Triangles. Elementary Functions. Similar Triangles. Similar Triangles

Trigonometry on Right Triangles. Elementary Functions. Similar Triangles. Similar Triangles Trigonometry on Right Triangles Trigonometry is introduced to students in two different forms, as functions on the unit circle and as functions on a right triangle. The unit circle approach is the most

More information

Mathematics 1. Lecture 5. Pattarawit Polpinit

Mathematics 1. Lecture 5. Pattarawit Polpinit Mathematics 1 Lecture 5 Pattarawit Polpinit Lecture Objective At the end of the lesson, the student is expected to be able to: familiarize with the use of Cartesian Coordinate System. determine the distance

More information

I. Model Problems II. Practice III. Challenge Problems IV. Answer Key

I. Model Problems II. Practice III. Challenge Problems IV. Answer Key On Twitter: twitter.com/engagingmath On FaceBook: www.mathworksheetsgo.com/facebook I. Model Problems II. Practice III. Challenge Problems IV. Answer Key Web Resources SOHCAHTAO www.mathwarehouse.com/trigonometry/sine-cosine-tangent-home.php

More information

Tessellations. A tessellation is created when a shape is repeated over and over again to cover the plane without any overlaps or gaps.

Tessellations. A tessellation is created when a shape is repeated over and over again to cover the plane without any overlaps or gaps. Tessellations Katherine Sheu A tessellation is created when a shape is repeated over and over again to cover the plane without any overlaps or gaps. 1. The picture below can be extended to a tessellation

More information

Geometry and Measurement

Geometry and Measurement The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

More information

INDEX. Arc Addition Postulate,

INDEX. Arc Addition Postulate, # 30-60 right triangle, 441-442, 684 A Absolute value, 59 Acute angle, 77, 669 Acute triangle, 178 Addition Property of Equality, 86 Addition Property of Inequality, 258 Adjacent angle, 109, 669 Adjacent

More information

Trigonometry. Week 1 Right Triangle Trigonometry

Trigonometry. Week 1 Right Triangle Trigonometry Trigonometry Introduction Trigonometry is the study of triangle measurement, but it has expanded far beyond that. It is not an independent subject of mathematics. In fact, it depends on your knowledge

More information

Due Tuesday, Oct 10, by 6 pm in your lab TF s mailbox

Due Tuesday, Oct 10, by 6 pm in your lab TF s mailbox Physics E-1a Expt 1: Measuring from a Distance Fall 2006 Due Tuesday, Oct 10, by 6 pm in your lab TF s mailbox Introduction There are many objects in the universe that simply aren't easy to measure. You

More information

6) Which of the following is closest to the length of the diagonal of a square that has sides that are 60 feet long?

6) Which of the following is closest to the length of the diagonal of a square that has sides that are 60 feet long? 1) The top of an 18-foot ladder touches the side of a building 14 feet above the ground. Approximately how far from the base of the building should the bottom of the ladder be placed? 4.0 feet 8.0 feet

More information

Right Triangles Test Review

Right Triangles Test Review Class: Date: Right Triangles Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. The triangle is not drawn

More information

How Do You Measure a Triangle? Examples

How Do You Measure a Triangle? Examples How Do You Measure a Triangle? Examples 1. A triangle is a three-sided polygon. A polygon is a closed figure in a plane that is made up of segments called sides that intersect only at their endpoints,

More information

GRAPHING (2 weeks) Main Underlying Questions: 1. How do you graph points?

GRAPHING (2 weeks) Main Underlying Questions: 1. How do you graph points? GRAPHING (2 weeks) The Rectangular Coordinate System 1. Plot ordered pairs of numbers on the rectangular coordinate system 2. Graph paired data to create a scatter diagram 1. How do you graph points? 2.

More information

Teaching & Learning Plans. Plan 8: Introduction to Trigonometry. Junior Certificate Syllabus

Teaching & Learning Plans. Plan 8: Introduction to Trigonometry. Junior Certificate Syllabus Teaching & Learning Plans Plan 8: Introduction to Trigonometry Junior Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes

More information

Section 2.1 Rectangular Coordinate Systems

Section 2.1 Rectangular Coordinate Systems P a g e 1 Section 2.1 Rectangular Coordinate Systems 1. Pythagorean Theorem In a right triangle, the lengths of the sides are related by the equation where a and b are the lengths of the legs and c is

More information

For each equation, identify the vertex, focus, axis of symmetry, and directrix. Then graph the parabola.

For each equation, identify the vertex, focus, axis of symmetry, and directrix. Then graph the parabola. For each equation, identify the vertex, focus, axis of symmetry, and directrix. Then graph the parabola. 1. (x 3) 2 = 12(y 7) The equation is in standard form and the squared term is x, which means that

More information

Section 8 Inverse Trigonometric Functions

Section 8 Inverse Trigonometric Functions Section 8 Inverse Trigonometric Functions Inverse Sine Function Recall that for every function y = f (x), one may de ne its INVERSE FUNCTION y = f 1 (x) as the unique solution of x = f (y). In other words,

More information

Write one or more equations to express the basic relationships between the variables.

Write one or more equations to express the basic relationships between the variables. Lecture 13 :Related Rates Please review Lecture 6; Modeling with Equations in our Algebra/Precalculus review on our web page. In this section, we look at situations where two or more variables are related

More information

MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane.

MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane. MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane. Symmetry When you can fold a figure in half, with both sides congruent, the fold line

More information

Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:

Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 Click the mouse button

More information

4.4 Right Triangle Trigonometry

4.4 Right Triangle Trigonometry 4.4 Right Triangle Trigonometry Trigonometry is introduced to students in two different forms, as functions on the unit circle and as functions on a right triangle. The unit circle approach is the most

More information

Solutions to Exercises, Section 5.1

Solutions to Exercises, Section 5.1 Instructor s Solutions Manual, Section 5.1 Exercise 1 Solutions to Exercises, Section 5.1 1. Find all numbers t such that ( 1 3,t) is a point on the unit circle. For ( 1 3,t)to be a point on the unit circle

More information

What s Your Angle? (Measurement)

What s Your Angle? (Measurement) The Middle School Math Project What s Your Angle? (Measurement) Objective Using inductive reasoning, students will devise procedures for using a protractor to measure the number of degrees in an angle.

More information

1.7 Find Perimeter, Circumference,

1.7 Find Perimeter, Circumference, .7 Find Perimeter, Circumference, and rea Goal p Find dimensions of polygons. Your Notes FORMULS FOR PERIMETER P, RE, ND CIRCUMFERENCE C Square Rectangle side length s length l and width w P 5 P 5 s 5

More information

Unit 2: Right Triangle Trigonometry RIGHT TRIANGLE RELATIONSHIPS

Unit 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 information

Right Triangle Trigonometry Test Review

Right Triangle Trigonometry Test Review Class: Date: Right Triangle Trigonometry Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. Leave your answer

More information

7.5 SYSTEMS OF INEQUALITIES. Copyright Cengage Learning. All rights reserved.

7.5 SYSTEMS OF INEQUALITIES. Copyright Cengage Learning. All rights reserved. 7.5 SYSTEMS OF INEQUALITIES Copyright Cengage Learning. All rights reserved. What You Should Learn Sketch the graphs of inequalities in two variables. Solve systems of inequalities. Use systems of inequalities

More information

3.1 Solving Systems Using Tables and Graphs

3.1 Solving Systems Using Tables and Graphs Algebra 2 Chapter 3 3.1 Solve Systems Using Tables & Graphs 3.1 Solving Systems Using Tables and Graphs A solution to a system of linear equations is an that makes all of the equations. To solve a system

More information

4) The length of one diagonal of a rhombus is 12 cm. The measure of the angle opposite that diagonal is 60º. What is the perimeter of the rhombus?

4) The length of one diagonal of a rhombus is 12 cm. The measure of the angle opposite that diagonal is 60º. What is the perimeter of the rhombus? Name Date Period MM2G1. Students will identify and use special right triangles. MM2G1a. Determine the lengths of sides of 30-60 -90 triangles. MM2G1b. Determine the lengths of sides of 45-45 -90 triangles.

More information

GEO420K Introduction To Field and Stratigraphic Methods Lab & Lecture Manual

GEO420K Introduction To Field and Stratigraphic Methods Lab & Lecture Manual 420k Lab #1 Compass and Pace & Compass Reading: 1) Measurement of Attitude and Location, p. 3-14. Appended to lab. 2) Compton, p. 16-21, 34-40, 75-80. 3) Web resources: see Lab 1 under www.geo.utexas.edu/courses/420k

More information

Vocabulary List Geometry Altitude- the perpendicular distance from the vertex to the opposite side of the figure (base)

Vocabulary List Geometry Altitude- the perpendicular distance from the vertex to the opposite side of the figure (base) GEOMETRY Vocabulary List Geometry Altitude- the perpendicular distance from the vertex to the opposite side of the figure (base) Face- one of the polygons of a solid figure Diagonal- a line segment that

More information

Right Triangles and SOHCAHTOA: Finding the Measure of an Angle Given any Two Sides (ONLY for ACUTE TRIANGLES Why?)

Right Triangles and SOHCAHTOA: Finding the Measure of an Angle Given any Two Sides (ONLY for ACUTE TRIANGLES Why?) Name Period Date Right Triangles and SOHCAHTOA: Finding the Measure of an Angle Given any Two Sides (ONLY for ACUTE TRIANGLES Why?) Preliminary Information: SOH CAH TOA is an acronym to represent the following

More information

TIgeometry.com. Geometry. Angle Bisectors in a Triangle

TIgeometry.com. Geometry. Angle Bisectors in a Triangle Angle Bisectors in a Triangle ID: 8892 Time required 40 minutes Topic: Triangles and Their Centers Use inductive reasoning to postulate a relationship between an angle bisector and the arms of the angle.

More information

Created by Ethan Fahy

Created by Ethan Fahy Created by Ethan Fahy To proceed to the next slide click the button. Next NCTM: Use trigonometric relationships to determine lengths and angle measures. NCTM: Use geometric ideas to solve problems in,

More information

Unit 6 Geometry: Constructing Triangles and Scale Drawings

Unit 6 Geometry: Constructing Triangles and Scale Drawings Unit 6 Geometry: Constructing Triangles and Scale Drawings Introduction In this unit, students will construct triangles from three measures of sides and/or angles, and will decide whether given conditions

More information

P A R A L L A X grades 9 1 2

P A R A L L A X grades 9 1 2 grades 9 1 2 Objective To demonstrate parallax and to show how the distance to an object can be calculated using mathematical principles related to parallax. Introduction The stars in the night sky all

More information

2.1 The Tangent Ratio

2.1 The Tangent Ratio 2.1 The Tangent Ratio In this Unit, we will study Right Angled Triangles. Right angled triangles are triangles which contain a right angle which measures 90 (the little box in the corner means that angle

More information

Where Do We Meet? Students will represent and analyze algebraically a wide variety of problem solving situations.

Where Do We Meet? Students will represent and analyze algebraically a wide variety of problem solving situations. Beth Yancey MAED 591 Where Do We Meet? Introduction: This lesson covers objectives in the algebra and geometry strands of the New York State standards for Algebra I. The students will use the graphs of

More information

Writing the Equation of a Line in Slope-Intercept Form

Writing the Equation of a Line in Slope-Intercept Form Writing the Equation of a Line in Slope-Intercept Form Slope-Intercept Form y = mx + b Example 1: Give the equation of the line in slope-intercept form a. With y-intercept (0, 2) and slope -9 b. Passing

More information

1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?

1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above? 1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width

More information

as a fraction and as a decimal to the nearest hundredth.

as a fraction and as a decimal to the nearest hundredth. Express each ratio as a fraction and as a decimal to the nearest hundredth. 1. sin A The sine of an angle is defined as the ratio of the opposite side to the hypotenuse. So, 2. tan C The tangent of an

More information

x = y + 2, and the line

x = y + 2, and the line WS 8.: Areas between Curves Name Date Period Worksheet 8. Areas between Curves Show all work on a separate sheet of paper. No calculator unless stated. Multiple Choice. Let R be the region in the first

More information

Chapter 9 Party Planner

Chapter 9 Party Planner Name: Date:. Given A 53, B 78, and a 6., use the Law of Sines to solve the triangle for the value of b. Round answer to two decimal places. C b a A c b sin a B sin A b 6. sin 78 sin 53 6.sin 78 b sin 53

More information

GEOMETRY CIRCLING THE BASES

GEOMETRY CIRCLING THE BASES LESSON 3: PRE-VISIT - PERIMETER AND AREA OBJECTIVE: Students will be able to: Distinguish between area and perimeter. Calculate the perimeter of a polygon whose side lengths are given or can be determined.

More information

Algebra Geometry Glossary. 90 angle

Algebra Geometry Glossary. 90 angle lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

More information

Heron s Formula. Key Words: Triangle, area, Heron s formula, angle bisectors, incenter

Heron s Formula. Key Words: Triangle, area, Heron s formula, angle bisectors, incenter Heron s Formula Lesson Summary: Students will investigate the Heron s formula for finding the area of a triangle. The lab has students find the area using three different methods: Heron s, the basic formula,

More information

θ. The angle is denoted in two ways: angle θ

θ. The angle is denoted in two ways: angle θ 1.1 Angles, Degrees and Special Triangles (1 of 24) 1.1 Angles, Degrees and Special Triangles Definitions An angle is formed by two rays with the same end point. The common endpoint is called the vertex

More information

Inverse Trigonometric Functions

Inverse Trigonometric Functions SECTION 4.7 Inverse Trigonometric Functions Copyright Cengage Learning. All rights reserved. Learning Objectives 1 2 3 4 Find the exact value of an inverse trigonometric function. Use a calculator to approximate

More information

Extra Credit Assignment Lesson plan. The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam.

Extra Credit Assignment Lesson plan. The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam. Extra Credit Assignment Lesson plan The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam. The extra credit assignment is to create a typed up lesson

More information

Two-Force Members, Three-Force Members, Distributed Loads

Two-Force Members, Three-Force Members, Distributed Loads Two-Force Members, Three-Force Members, Distributed Loads Two-Force Members - Examples ME 202 2 Two-Force Members Only two forces act on the body. The line of action (LOA) of forces at both A and B must

More information

Trigonometry Notes Sarah Brewer Alabama School of Math and Science. Last Updated: 25 November 2011

Trigonometry Notes Sarah Brewer Alabama School of Math and Science. Last Updated: 25 November 2011 Trigonometry Notes Sarah Brewer Alabama School of Math and Science Last Updated: 25 November 2011 6 Basic Trig Functions Defined as ratios of sides of a right triangle in relation to one of the acute angles

More information

Indirect Measurement Technique: Using Trigonometric Ratios Grade Nine

Indirect Measurement Technique: Using Trigonometric Ratios Grade Nine Ohio Standards Connections Measurement Benchmark D Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve

More information

The American School of Marrakesh. Geometry Geometry Summer Preparation Packet

The American School of Marrakesh. Geometry Geometry Summer Preparation Packet The American School of Marrakesh Geometry Geometry Summer Preparation Packet Summer 2016 Geometry Summer Preparation Packet This summer packet contains exciting math problems designed to ensure your readiness

More information

Solution Guide for Chapter 6: The Geometry of Right Triangles

Solution Guide for Chapter 6: The Geometry of Right Triangles Solution Guide for Chapter 6: The Geometry of Right Triangles 6. THE THEOREM OF PYTHAGORAS E-. Another demonstration: (a) Each triangle has area ( ). ab, so the sum of the areas of the triangles is 4 ab

More information

A Review of Vector Addition

A Review of Vector Addition Motion and Forces in Two Dimensions Sec. 7.1 Forces in Two Dimensions 1. A Review of Vector Addition. Forces on an Inclined Plane 3. How to find an Equilibrant Vector 4. Projectile Motion Objectives Determine

More information

Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.

Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same. Chapter 11: Areas of Plane Figures (page 422) 11-1: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length

More information

Chapter 3. Chapter 3 Opener. Section 3.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 101) So, the value of x is 112.

Chapter 3. Chapter 3 Opener. Section 3.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 101) So, the value of x is 112. Chapter 3 Opener Try It Yourself (p. 101) 1. The angles are vertical. x + 8 120 x 112 o, the value of x is 112. 2. The angles are adjacent. ( x ) + 3 + 43 90 x + 46 90 x 44 o, the value of x is 44. 3.

More information

CLIL MultiKey lesson plan

CLIL MultiKey lesson plan LESSON PLAN Subject: Mathematics Topic: Triangle Age of students: 16 Language level: B1, B2 Time: 45-60 min Contents aims: After completing the lesson, the student will be able to: Classify and compare

More information

Perform and describe the rotation of a shape around a centre that is on the shape.

Perform and describe the rotation of a shape around a centre that is on the shape. 1 Describing Rotations Perform and describe the rotation of a shape around a centre that is on the shape. You will need a ruler and a protractor. 1. Describe the rotation of this shape. The black dot on

More information

11 Trigonometric Functions of Acute Angles

11 Trigonometric Functions of Acute Angles Arkansas Tech University MATH 10: Trigonometry Dr. Marcel B. Finan 11 Trigonometric Functions of Acute Angles In this section you will learn (1) how to find the trigonometric functions using right triangles,

More information

Chapter 8 Geometry We will discuss following concepts in this chapter.

Chapter 8 Geometry We will discuss following concepts in this chapter. Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles

More information

Sixth Grade Math Pacing Guide Page County Public Schools MATH 6/7 1st Nine Weeks: Days Unit: Decimals B

Sixth Grade Math Pacing Guide Page County Public Schools MATH 6/7 1st Nine Weeks: Days Unit: Decimals B Sixth Grade Math Pacing Guide MATH 6/7 1 st Nine Weeks: Unit: Decimals 6.4 Compare and order whole numbers and decimals using concrete materials, drawings, pictures and mathematical symbols. 6.6B Find

More information

Common Core Unit Summary Grades 6 to 8

Common Core Unit Summary Grades 6 to 8 Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations

More information

opposite side adjacent side sec A = hypotenuse opposite side adjacent side = a b

opposite side adjacent side sec A = hypotenuse opposite side adjacent side = a b Trigonometry Angles & Circular Functions: Solving Right Triangles Trigonometric Functions in a Right Triangle We have already looked at the trigonometric functions from the perspective of the unit circle.

More information

y = rsin! (opp) x = z cos! (adj) sin! = y z = The Other Trig Functions

y = rsin! (opp) x = z cos! (adj) sin! = y z = The Other Trig Functions MATH 7 Right Triangle Trig Dr. Neal, WKU Previously, we have seen the right triangle formulas x = r cos and y = rsin where the hypotenuse r comes from the radius of a circle, and x is adjacent to and y

More information

exponents order of operations expression base scientific notation SOL 8.1 Represents repeated multiplication of the number.

exponents order of operations expression base scientific notation SOL 8.1 Represents repeated multiplication of the number. SOL 8.1 exponents order of operations expression base scientific notation Represents repeated multiplication of the number. 10 4 Defines the order in which operations are performed to simplify an expression.

More information

Calculus with Analytic Geometry I Exam 10 Take Home part

Calculus with Analytic Geometry I Exam 10 Take Home part Calculus with Analytic Geometry I Exam 10 Take Home part Textbook, Section 47, Exercises #22, 30, 32, 38, 48, 56, 70, 76 1 # 22) Find, correct to two decimal places, the coordinates of the point on the

More information

8-3 Dot Products and Vector Projections

8-3 Dot Products and Vector Projections 8-3 Dot Products and Vector Projections Find the dot product of u and v Then determine if u and v are orthogonal 1u =, u and v are not orthogonal 2u = 3u =, u and v are not orthogonal 6u = 11i + 7j; v

More information

MEMORANDUM. All students taking the CLC Math Placement Exam PLACEMENT INTO CALCULUS AND ANALYTIC GEOMETRY I, MTH 145:

MEMORANDUM. All students taking the CLC Math Placement Exam PLACEMENT INTO CALCULUS AND ANALYTIC GEOMETRY I, MTH 145: MEMORANDUM To: All students taking the CLC Math Placement Eam From: CLC Mathematics Department Subject: What to epect on the Placement Eam Date: April 0 Placement into MTH 45 Solutions This memo is an

More information

Chapter 8. Right Triangles

Chapter 8. Right Triangles Chapter 8 Right Triangles Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately apply the

More information

Applications of Right Triangle Trigonometry: Angles of Elevation and Depression

Applications of Right Triangle Trigonometry: Angles of Elevation and Depression Applications of Right Triangle Trigonometry: Angles of Elevation and Depression Preliminary Information: On most maps, it is customary to orient oneself relative to the direction north: for this reason,

More information

Centroid: The point of intersection of the three medians of a triangle. Centroid

Centroid: The point of intersection of the three medians of a triangle. Centroid Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:

More information

1.3 Displacement in Two Dimensions

1.3 Displacement in Two Dimensions 1.3 Displacement in Two Dimensions So far, you have learned about motion in one dimension. This is adequate for learning basic principles of kinematics, but it is not enough to describe the motions of

More information

The Protractor Postulate and the SAS Axiom. Chapter The Axioms of Plane Geometry

The Protractor Postulate and the SAS Axiom. Chapter The Axioms of Plane Geometry The Protractor Postulate and the SAS Axiom Chapter 3.4-3.7 The Axioms of Plane Geometry The Protractor Postulate and Angle Measure The Protractor Postulate (p51) defines the measure of an angle (denoted

More information

CK-12 Geometry: Midpoints and Bisectors

CK-12 Geometry: Midpoints and Bisectors CK-12 Geometry: Midpoints and Bisectors Learning Objectives Identify the midpoint of line segments. Identify the bisector of a line segment. Understand and the Angle Bisector Postulate. Review Queue Answer

More information

Angles and Quadrants. Angle Relationships and Degree Measurement. Chapter 7: Trigonometry

Angles and Quadrants. Angle Relationships and Degree Measurement. Chapter 7: Trigonometry Chapter 7: Trigonometry Trigonometry is the study of angles and how they can be used as a means of indirect measurement, that is, the measurement of a distance where it is not practical or even possible

More information

Examples of Scalar and Vector Quantities 1. Candidates should be able to : QUANTITY VECTOR SCALAR

Examples of Scalar and Vector Quantities 1. Candidates should be able to : QUANTITY VECTOR SCALAR Candidates should be able to : Examples of Scalar and Vector Quantities 1 QUANTITY VECTOR SCALAR Define scalar and vector quantities and give examples. Draw and use a vector triangle to determine the resultant

More information

Example #1: f(x) = x 2. Sketch the graph of f(x) and determine if it passes VLT and HLT. Is the inverse of f(x) a function?

Example #1: f(x) = x 2. Sketch the graph of f(x) and determine if it passes VLT and HLT. Is the inverse of f(x) a function? Unit 3 Eploring Inverse trig. functions Standards: F.BF. Find inverse functions. F.BF.d (+) Produce an invertible function from a non invertible function by restricting the domain. F.TF.6 (+) Understand

More information

Teaching & Learning Plans. Using Pythagoras Theorem to establish the Distance Formula (Draft) Junior Certificate Syllabus

Teaching & Learning Plans. Using Pythagoras Theorem to establish the Distance Formula (Draft) Junior Certificate Syllabus Teaching & Learning Plans Using Pythagoras Theorem to establish the Distance Formula (Draft) Junior Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson,

More information

A convex polygon is a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon.

A convex polygon is a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon. hapter 7 Polygons A polygon can be described by two conditions: 1. No two segments with a common endpoint are collinear. 2. Each segment intersects exactly two other segments, but only on the endpoints.

More information