Right Triangle Trigonometry Test Review
|
|
|
- Oswin Cain
- 7 years ago
- Views:
Transcription
1 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 in simplest radical form. 2. a. 17 m b. 113 m c. 113 m d. 71 m a cm b cm c. 21 cm d. 3 cm 3. A grid shows the positions of a subway stop and your house. The subway stop is located at ( 5, 2) and your house is located at ( 9, 9). What is the distance, to the nearest unit, between your house and the subway stop? a. 5 b. 13 c. 8 d A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain. a. yes; c. no; b. no; = 19 2 d. yes; = A triangle has side lengths of 10 cm, 24 cm, and 33 cm. Classify it as acute, obtuse, or right. a. acute b. right c. obtuse 1
2 6. In triangle ABC, A is a right angle and m B = 45. Find BC. If you answer is not an integer, leave it in simplest radical form. a. 22 ft b ft c. 11 ft d ft 7. Find the length of the hypotenuse. a. 12 b. 6 c. 5 d Find the length of the leg. If your answer is not an integer, leave it in simplest radical form. a. 128 b. 8 2 c. 16 d Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. a. x = 7, y = 9.9 b. x = 9.9, y = 7 c. x = 4.9, y = 6.1 d. x = 6.1, y = 4.9 2
3 10. The area of a square garden is 50 m 2. How long is the diagonal? a. 25 m b. 100 m c. 5 6 m d. 10 m Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. 11. a. 2 b c. 1 2 d a. x = 17, y = 34 3 c. x = 34 3, y = 17 b. x = 34, y = 17 3 d. x = 17 3, y = The length of the hypotenuse of a triangle is 4. Find the perimeter. a c b d A piece of art is in the shape of an equilateral triangle with sides of 7 in. Find the area of the piece of art. Round your answer to the nearest tenth. a. none of these b in. 2 c in. 2 d in A sign is in the shape of a rhombus with a 60 angle and sides of 9 cm long. Find its area to the nearest tenth. a cm 2 b. 3.9 cm 2 c. 7.8 cm 2 d cm 2 3
4 16. Write the tangent ratios for Y and Z. a. tan Y = 6 7 ; tan Z = 7 6 c. tan Y = 7 6 ; tan Z = 6 7 b. tan Y = 85 7 ; tan Z = 85 6 d. tan Y = 7 85 ; tan Z = 6 85 Find the value of x. Round your answer to the nearest tenth. 17. a. 3.5 b c. 6.1 d a. 3.3 b. 3.1 c d
5 19. a. 6.2 cm b cm c cm d cm Find the value of x to the nearest degree. 20. a. 30 b. 60 c. 70 d a. 67 b. 23 c. 83 d Find the value of w, then x. Round lengths of segments to the nearest tenth. a. w = 13.3, x = 10.2 c. w = 13.3, x = 23.6 b. w = 10.8, x = 6.1 d. w = 10.8, x = Find the missing value to the nearest hundredth. a b c d
6 24. Write the ratios for sin X and cos X. a. sin X = 119 5, cos X = c. sin X = b. sin X = 119, cos X = 5 d. sin X = , cos X = , cos X = Find the value of x. Round to the nearest degree. 25. a. 55 b. 35 c. 30 d a. 41 b. 36 c. 46 d Viola drives 170 meters up a hill that makes an angle of 6 with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered? a m b m c m d m 6
7 28. Find the value of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree. 29. a. w = 7.7, x = 44 c. w = 7.7, x = 54 b. w = 6.4, x = 54 d. w = 6.4, x = 44 Find the value of x. Round the length to the nearest tenth. 30. a. 7.1 cm b cm c. 9.2 cm d. 8.4 cm 31. a m b m c. 8.6 m d m a. 7.6 ft b ft c ft d. 7.9 ft 7
8 32. a m b m c m d m 33. a yd b yd c. 9 yd d yd 34. To approach the runway, a small plane must begin a 9 descent starting from a height of 1125 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach? a. 1.3 mi b. 1.4 mi c. 0.2 mi d. 7,191.5 mi 35. A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the entrance door? a. 39 b. 51 c. 53 d Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree. a. 54 b. 36 c. 46 d. 44 8
9 Short Answer 37. A highway makes an angle of 6 with the horizontal. This angle is maintained for a horizontal distance of 8 miles. a. Draw and label a diagram to represent this situation. b. To the nearest hundredth of a mile, how high does the highway rise in this 8-mile section? Show the steps you use to find the distance. 38. A forest ranger spots a fire from a 21-foot tower. The angle of depression from the tower to the fire is 12. a. Draw a diagram to represent this situation. b. To the nearest foot, how far is the fire from the base of the tower? Show the steps you use to find the solution. 9
10 Right Triangle Trigonometry Test Review Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: The Pythagorean Theorem NAT: NAEP 2005 G3d ADP I.4.1 ADP J.1.6 ADP K.1.2 ADP K.5 ADP K.10.3 STA: NJ A.1 NJ B.1 NJ A.1 NJ A.4c NJ D.1 NJ E.1b TOP: 8-1 Example 2 KEY: Pythagorean Theorem leg hypotenuse 2. ANS: B PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: The Pythagorean Theorem NAT: NAEP 2005 G3d ADP I.4.1 ADP J.1.6 ADP K.1.2 ADP K.5 ADP K.10.3 STA: NJ A.1 NJ B.1 NJ A.1 NJ A.4c NJ D.1 NJ E.1b TOP: 8-1 Example 2 KEY: Pythagorean Theorem leg hypotenuse 3. ANS: C PTS: 1 DIF: L3 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: The Pythagorean Theorem NAT: NAEP 2005 G3d ADP I.4.1 ADP J.1.6 ADP K.1.2 ADP K.5 ADP K.10.3 STA: NJ A.1 NJ B.1 NJ A.1 NJ A.4c NJ D.1 NJ E.1b TOP: 8-1 Example 3 KEY: Pythagorean Theorem leg hypotenuse word problem problem solving 4. ANS: C PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: The Converse of the Pythagorean Theorem NAT: NAEP 2005 G3d ADP I.4.1 ADP J.1.6 ADP K.1.2 ADP K.5 ADP K.10.3 STA: NJ A.1 NJ B.1 NJ A.1 NJ A.4c NJ D.1 NJ E.1b TOP: 8-1 Example 4 KEY: Pythagorean Theorem 5. ANS: C PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: The Converse of the Pythagorean Theorem NAT: NAEP 2005 G3d ADP I.4.1 ADP J.1.6 ADP K.1.2 ADP K.5 ADP K.10.3 STA: NJ A.1 NJ B.1 NJ A.1 NJ A.4c NJ D.1 NJ E.1b TOP: 8-1 Example 5 KEY: right triangle obtuse triangle acute triangle 6. ANS: D PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles OBJ: Triangles NAT: NAEP 2005 G3d ADP I.4.1 ADP J.5.1 ADP K.5 TOP: 8-2 Example 1 KEY: special right triangles 7. ANS: B PTS: 1 DIF: L2 REF: 8-2 Special Right Triangles OBJ: Triangles NAT: NAEP 2005 G3d ADP I.4.1 ADP J.5.1 ADP K.5 TOP: 8-2 Example 1 KEY: special right triangles hypotenuse 8. ANS: B PTS: 1 DIF: L2 REF: 8-2 Special Right Triangles OBJ: Triangles NAT: NAEP 2005 G3d ADP I.4.1 ADP J.5.1 ADP K.5 TOP: 8-2 Example 2 KEY: special right triangles hypotenuse leg 1
11 9. ANS: B PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles OBJ: Triangles NAT: NAEP 2005 G3d ADP I.4.1 ADP J.5.1 ADP K.5 TOP: 8-2 Example 2 KEY: special right triangles hypotenuse leg 10. ANS: D PTS: 1 DIF: L2 REF: 8-2 Special Right Triangles OBJ: Triangles NAT: NAEP 2005 G3d ADP I.4.1 ADP J.5.1 ADP K.5 TOP: 8-2 Example 3 KEY: special right triangles diagonal 11. ANS: D PTS: 1 DIF: L2 REF: 8-2 Special Right Triangles OBJ: Using Triangles NAT: NAEP 2005 G3d ADP I.4.1 ADP J.5.1 ADP K.5 TOP: 8-2 Example 4 KEY: special right triangles leg hypotenuse 12. ANS: D PTS: 1 DIF: L2 REF: 8-2 Special Right Triangles OBJ: Using Triangles NAT: NAEP 2005 G3d ADP I.4.1 ADP J.5.1 ADP K.5 TOP: 8-2 Example 4 KEY: special right triangles leg hypotenuse 13. ANS: B PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles OBJ: Using Triangles NAT: NAEP 2005 G3d ADP I.4.1 ADP J.5.1 ADP K.5 TOP: 8-2 Example 4 KEY: special right triangles perimeter 14. ANS: D PTS: 1 DIF: L2 REF: 8-2 Special Right Triangles OBJ: Using Triangles NAT: NAEP 2005 G3d ADP I.4.1 ADP J.5.1 ADP K.5 TOP: 8-2 Example 5 KEY: area of a triangle word problem problem solving 15. ANS: A PTS: 1 DIF: L2 REF: 8-2 Special Right Triangles OBJ: Using Triangles NAT: NAEP 2005 G3d ADP I.4.1 ADP J.5.1 ADP K.5 TOP: 8-2 Example 5 KEY: rhombus word problem problem solving 16. ANS: C PTS: 1 DIF: L3 REF: 8-3 The Tangent Ratio TOP: 8-3 Example 1 KEY: leg adjacent to angle leg opposite angle tangent tangent ratio 17. ANS: D PTS: 1 DIF: L2 REF: 8-3 The Tangent Ratio TOP: 8-3 Example 2 KEY: side length using tangent tangent tangent ratio 18. ANS: C PTS: 1 DIF: L2 REF: 8-3 The Tangent Ratio TOP: 8-3 Example 2 KEY: side length using tangent tangent tangent ratio 2
12 19. ANS: A PTS: 1 DIF: L3 REF: 8-3 The Tangent Ratio TOP: 8-3 Example 2 KEY: side length using tangent tangent tangent ratio 20. ANS: B PTS: 1 DIF: L2 REF: 8-3 The Tangent Ratio TOP: 8-3 Example 3 KEY: inverse of tangent tangent tangent ratio angle measure using tangent 21. ANS: B PTS: 1 DIF: L3 REF: 8-3 The Tangent Ratio TOP: 8-3 Example 3 KEY: inverse of tangent tangent tangent ratio angle measure using tangent 22. ANS: A PTS: 1 DIF: L3 REF: 8-3 The Tangent Ratio TOP: 8-3 Example 2 KEY: tangent side length using tangent tangent ratio problem solving 23. ANS: C PTS: 1 DIF: L3 REF: 8-3 The Tangent Ratio TOP: 8-3 Example 3 KEY: angle measure using tangent 24. ANS: C PTS: 1 DIF: L3 REF: 8-4 Sine and Cosine Ratios OBJ: Using Sine and Cosine in Triangles TOP: 8-4 Example 1 KEY: cosine sine sine ratio cosine ratio 25. ANS: B PTS: 1 DIF: L2 REF: 8-4 Sine and Cosine Ratios OBJ: Using Sine and Cosine in Triangles TOP: 8-4 Example 3 KEY: inverse of cosine and sine angle measure using sine and cosine sine 26. ANS: D PTS: 1 DIF: L2 REF: 8-4 Sine and Cosine Ratios OBJ: Using Sine and Cosine in Triangles TOP: 8-4 Example 3 KEY: inverse of cosine and sine angle measure using sine and cosine cosine 3
13 27. ANS: B PTS: 1 DIF: L3 REF: 8-4 Sine and Cosine Ratios OBJ: Using Sine and Cosine in Triangles TOP: 8-4 Example 2 KEY: cosine word problem side length using since and cosine problem solving cosine ratio 28. ANS: A PTS: 1 DIF: L3 REF: 8-4 Sine and Cosine Ratios OBJ: Using Sine and Cosine in Triangles KEY: side length using since and cosine angle measure using sine and cosine problem solving sine inverse of cosine and sine sine ratio 29. ANS: C PTS: 1 DIF: L2 TOP: 8-5 Example 2 KEY: tangent side length using tangent tangent ratio 30. ANS: C PTS: 1 DIF: L2 TOP: 8-5 Example 2 KEY: sine side length using since and cosine sine ratio 31. ANS: D PTS: 1 DIF: L2 TOP: 8-5 Example 2 KEY: cosine side length using since and cosine cosine ratio 32. ANS: B PTS: 1 DIF: L2 TOP: 8-5 Example 3 KEY: sine side length using since and cosine sine ratio angles of elevation and depression 33. ANS: B PTS: 1 DIF: L2 TOP: 8-5 Example 3 KEY: tangent side length using tangent tangent ratio angles of elevation and depression 4
14 34. ANS: B PTS: 1 DIF: L2 TOP: 8-5 Example 3 KEY: side length using since and cosine word problem problem solving sine angles of elevation and depression sine ratio 35. ANS: A PTS: 1 DIF: L3 KEY: angle measure using tangent word problem angles of elevation and depression problem solving tangent inverse of tangent tangent ratio 36. ANS: B PTS: 1 DIF: L3 KEY: angle measure using tangent word problem angles of elevation and depression problem solving inverse of tangent tangent ratio SHORT ANSWER 37. ANS: a. b. tan 6 = x 8 Use the tangent ratio. x = 8(tan 6 ) Solve for x. x 0.84 The rise is about 0.84 miles. PTS: 1 DIF: L3 REF: 8-3 The Tangent Ratio TOP: 8-3 Example 2 KEY: problem solving word problem tangent side length using tangent tangent ratio multi-part question 5
15 38. ANS: a. b. tan 12 = 21 Use the tangent ratio. x 21 x = Solve for x. tan 12 x 99 The fire is about 99 feet from the base of the tower. PTS: 1 DIF: L3 TOP: 8-5 Example 2 KEY: side length using tangent word problem multi-part question problem solving tangent angles of elevation and depression tangent ratio 6
Pythagorean Theorem: 9. x 2 2
Geometry Chapter 8 - Right Triangles.7 Notes on Right s Given: any 3 sides of a Prove: the is acute, obtuse, or right (hint: use the converse of Pythagorean Theorem) If the (longest side) 2 > (side) 2
How To Solve The Pythagorean Triangle
Name Period CHAPTER 9 Right Triangles and Trigonometry Section 9.1 Similar right Triangles Objectives: Solve problems involving similar right triangles. Use a geometric mean to solve problems. Ex. 1 Use
Law of Cosines. If the included angle is a right angle then the Law of Cosines is the same as the Pythagorean Theorem.
Law of Cosines In the previous section, we learned how the Law of Sines could be used to solve oblique triangles in three different situations () where a side and two angles (SAA) were known, () where
Section 7.1 Solving Right Triangles
Section 7.1 Solving Right Triangles Note that a calculator will be needed for most of the problems we will do in class. Test problems will involve angles for which no calculator is needed (e.g., 30, 45,
Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. 9) 179
Trigonometry Chapters 1 & 2 Test 1 Name Provide an appropriate response. 1) Find the supplement of an angle whose measure is 7. Find the measure of each angle in the problem. 2) Perform the calculation.
RIGHT TRIANGLE TRIGONOMETRY
RIGHT TRIANGLE TRIGONOMETRY The word Trigonometry can be broken into the parts Tri, gon, and metry, which means Three angle measurement, or equivalently Triangle measurement. Throughout this unit, we will
Parallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular.
CONDENSED L E S S O N. Parallel and Perpendicular In this lesson you will learn the meaning of parallel and perpendicular discover how the slopes of parallel and perpendicular lines are related use slopes
Square Roots and the Pythagorean Theorem
4.8 Square Roots and the Pythagorean Theorem 4.8 OBJECTIVES 1. Find the square root of a perfect square 2. Use the Pythagorean theorem to find the length of a missing side of a right triangle 3. Approximate
Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Class: Date: ID: A Q3 Geometry Review Multiple Choice Identify the choice that best completes the statement or answers the question. Graph the image of each figure under a translation by the given
Geometry Notes RIGHT TRIANGLE TRIGONOMETRY
Right Triangle Trigonometry Page 1 of 15 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
http://www.castlelearning.com/review/teacher/assignmentprinting.aspx 5. 2 6. 2 1. 10 3. 70 2. 55 4. 180 7. 2 8. 4
of 9 1/28/2013 8:32 PM Teacher: Mr. Sime Name: 2 What is the slope of the graph of the equation y = 2x? 5. 2 If the ratio of the measures of corresponding sides of two similar triangles is 4:9, then the
Geometry: Classifying, Identifying, and Constructing Triangles
Geometry: Classifying, Identifying, and Constructing Triangles Lesson Objectives Teacher's Notes Lesson Notes 1) Identify acute, right, and obtuse triangles. 2) Identify scalene, isosceles, equilateral
Cumulative Test. 161 Holt Geometry. Name Date Class
Choose the best answer. 1. P, W, and K are collinear, and W is between P and K. PW 10x, WK 2x 7, and PW WK 6x 11. What is PK? A 2 C 90 B 6 D 11 2. RM bisects VRQ. If mmrq 2, what is mvrm? F 41 H 9 G 2
GEOMETRY B: CIRCLE TEST PRACTICE
Class: Date: GEOMETRY B: CIRCLE TEST PRACTICE Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the measures of the indicated angles. Which statement
9 Right Triangle Trigonometry
www.ck12.org CHAPTER 9 Right Triangle Trigonometry Chapter Outline 9.1 THE PYTHAGOREAN THEOREM 9.2 CONVERSE OF THE PYTHAGOREAN THEOREM 9.3 USING SIMILAR RIGHT TRIANGLES 9.4 SPECIAL RIGHT TRIANGLES 9.5
Applications for Triangles
Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given
(15.) To find the distance from point A to point B across. a river, a base line AC is extablished. AC is 495 meters
(15.) To find the distance from point A to point B across a river, a base line AC is extablished. AC is 495 meters long. Angles
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
TRIGONOMETRY OF THE RIGHT TRIANGLE
HPTER 8 HPTER TLE OF ONTENTS 8-1 The Pythagorean Theorem 8-2 The Tangent Ratio 8-3 pplications of the Tangent Ratio 8-4 The Sine and osine Ratios 8-5 pplications of the Sine and osine Ratios 8-6 Solving
Right Triangles 4 A = 144 A = 16 12 5 A = 64
Right Triangles If I looked at enough right triangles and experimented a little, I might eventually begin to notice a relationship developing if I were to construct squares formed by the legs of a right
4.3 & 4.8 Right Triangle Trigonometry. Anatomy of Right Triangles
4.3 & 4.8 Right Triangle Trigonometry Anatomy of Right Triangles The right triangle shown at the right uses lower case a, b and c for its sides with c being the hypotenuse. The sides a and b are referred
10.2 45-45 -90 Triangles
Page of 6 0. --0 Triangles Goal Find the side lengths of --0 triangles. Key Words --0 triangle isosceles triangle p. 7 leg of a right triangle p. hypotenuse p. Geo-Activity Eploring an Isosceles Right
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
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
Introduction and Mathematical Concepts
CHAPTER 1 Introduction and Mathematical Concepts PREVIEW In this chapter you will be introduced to the physical units most frequently encountered in physics. After completion of the chapter you will be
HS Mathematics Item Specification C1 TO
Task Model 1 Multiple Choice, single correct response G-SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of acute
Right Triangles A right triangle, as the one shown in Figure 5, is a triangle that has one angle measuring
Page 1 9 Trigonometry of Right Triangles Right Triangles A right triangle, as the one shown in Figure 5, is a triangle that has one angle measuring 90. The side opposite to the right angle is the longest
Basic Lesson: Pythagorean Theorem
Basic Lesson: Pythagorean Theorem Basic skill One leg of a triangle is 10 cm and other leg is of 24 cm. Find out the hypotenuse? Here we have AB = 10 and BC = 24 Using the Pythagorean Theorem AC 2 = AB
Geometry Module 4 Unit 2 Practice Exam
Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning
Geometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
Lesson 1: Exploring Trigonometric Ratios
Lesson 1: Exploring Trigonometric Ratios Common Core Georgia Performance Standards MCC9 12.G.SRT.6 MCC9 12.G.SRT.7 Essential Questions 1. How are the properties of similar triangles used to create trigonometric
MCA Formula Review Packet
MCA Formula Review Packet 1 3 4 5 6 7 The MCA-II / BHS Math Plan Page 1 of 15 Copyright 005 by Claude Paradis 8 9 10 1 11 13 14 15 16 17 18 19 0 1 3 4 5 6 7 30 8 9 The MCA-II / BHS Math Plan Page of 15
Introduction Assignment
PRE-CALCULUS 11 Introduction Assignment Welcome to PREC 11! This assignment will help you review some topics from a previous math course and introduce you to some of the topics that you ll be studying
25 The Law of Cosines and Its Applications
Arkansas Tech University MATH 103: Trigonometry Dr Marcel B Finan 5 The Law of Cosines and Its Applications The Law of Sines is applicable when either two angles and a side are given or two sides and an
Lesson 33: Example 1 (5 minutes)
Student Outcomes Students understand that the Law of Sines can be used to find missing side lengths in a triangle when you know the measures of the angles and one side length. Students understand that
Applications of the Pythagorean Theorem
9.5 Applications of the Pythagorean Theorem 9.5 OBJECTIVE 1. Apply the Pythagorean theorem in solving problems Perhaps the most famous theorem in all of mathematics is the Pythagorean theorem. The theorem
Trigonometry. An easy way to remember trigonometric properties is:
Trigonometry It is possible to solve many force and velocity problems by drawing vector diagrams. However, the degree of accuracy is dependent upon the exactness of the person doing the drawing and measuring.
6.1 Basic Right Triangle Trigonometry
6.1 Basic Right Triangle Trigonometry MEASURING ANGLES IN RADIANS First, let s introduce the units you will be using to measure angles, radians. A radian is a unit of measurement defined as the angle at
Pythagoras Theorem. Page I can... 1... identify and label right-angled triangles. 2... explain Pythagoras Theorem. 4... calculate the hypotenuse
Pythagoras Theorem Page I can... 1... identify and label right-angled triangles 2... eplain Pythagoras Theorem 4... calculate the hypotenuse 5... calculate a shorter side 6... determine whether a triangle
Georgia Online Formative Assessment Resource (GOFAR) AG geometry domain
AG geometry domain Name: Date: Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 36 ) 1. Amy drew a circle graph to represent
Definitions, Postulates and Theorems
Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven
Section 2.4 Law of Sines and Cosines
Section.4 Law of Sines and osines Oblique Triangle A triangle that is not a right triangle, either acute or obtuse. The measures of the three sides and the three angles of a triangle can be found if at
Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round to two decimal places.
SECTION.1 Simplify. 1. 7π π. 5π 6 + π Find the measure of the angle in degrees between the hour hand and the minute hand of a clock at the time shown. Measure the angle in the clockwise direction.. 1:0.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Santa Monica College COMPASS Geometry Sample Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the area of the shaded region. 1) 5 yd 6 yd
Lesson 18 Pythagorean Triples & Special Right Triangles
Student Name: Date: Contact Person Name: Phone Number: Teas Assessment of Knowledge and Skills Eit Level Math Review Lesson 18 Pythagorean Triples & Special Right Triangles TAKS Objective 6 Demonstrate
PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
Algebra 2 Chapter 5 Practice Test (Review)
Name: Class: Date: Algebra 2 Chapter 5 Practice Test (Review) Multiple Choice Identify the choice that best completes the statement or answers the question. Determine whether the function is linear or
Tallahassee Community College PERIMETER
Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides
Sample Test Questions
mathematics College Algebra Geometry Trigonometry Sample Test Questions A Guide for Students and Parents act.org/compass Note to Students Welcome to the ACT Compass Sample Mathematics Test! You are about
2312 test 2 Fall 2010 Form B
2312 test 2 Fall 2010 Form B 1. Write the slope-intercept form of the equation of the line through the given point perpendicular to the given lin point: ( 7, 8) line: 9x 45y = 9 2. Evaluate the function
Right Triangle Trigonometry
Section 6.4 OBJECTIVE : Right Triangle Trigonometry Understanding the Right Triangle Definitions of the Trigonometric Functions otenuse osite side otenuse acent side acent side osite side We will be concerned
Geometry Regents Review
Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest
1 Introduction to Basic Geometry
1 Introduction to Basic Geometry 1.1 Euclidean Geometry and Axiomatic Systems 1.1.1 Points, Lines, and Line Segments Geometry is one of the oldest branches of mathematics. The word geometry in the Greek
8-5 Angles of Elevation and Depression. The length of the base of the ramp is about 27.5 ft.
1.BIKING Lenora wants to build the bike ramp shown. Find the length of the base of the ramp. The length of the base of the ramp is about 27.5 ft. ANSWER: 27.5 ft 2.BASEBALL A fan is seated in the upper
Conjectures for Geometry for Math 70 By I. L. Tse
Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:
" Angles ABCand DEFare congruent
Collinear points a) determine a plane d) are vertices of a triangle b) are points of a circle c) are coplanar 2. Different angles that share a common vertex point cannot a) share a common angle side! b)
Pre-Algebra Lesson 6-1 to 6-3 Quiz
Pre-lgebra Lesson 6-1 to 6-3 Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the area of the triangle. 17 ft 74 ft Not drawn to scale a. 629 ft
The common ratio in (ii) is called the scaled-factor. An example of two similar triangles is shown in Figure 47.1. Figure 47.1
47 Similar Triangles An overhead projector forms an image on the screen which has the same shape as the image on the transparency but with the size altered. Two figures that have the same shape but not
Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.
Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles
Quick Reference ebook
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed
Geometry EOC Practice Test #2
Class: Date: Geometry EOC Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Rebecca is loading medical supply boxes into a crate. Each supply
Set 4: Special Congruent Triangles Instruction
Instruction Goal: To provide opportunities for students to develop concepts and skills related to proving right, isosceles, and equilateral triangles congruent using real-world problems Common Core Standards
High School Geometry Test Sampler Math Common Core Sampler Test
High School Geometry Test Sampler Math Common Core Sampler Test Our High School Geometry sampler covers the twenty most common questions that we see targeted for this level. For complete tests and break
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
Mathematics (Project Maths Phase 1)
2011. S133S Coimisiún na Scrúduithe Stáit State Examinations Commission Junior Certificate Examination Sample Paper Mathematics (Project Maths Phase 1) Paper 2 Ordinary Level Time: 2 hours 300 marks Running
of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
Math. Rounding Decimals. Answers. 1) Round to the nearest tenth. 8.54 8.5. 2) Round to the nearest whole number. 99.59 100
1) Round to the nearest tenth. 8.54 8.5 2) Round to the nearest whole number. 99.59 100 3) Round to the nearest tenth. 310.286 310.3 4) Round to the nearest whole number. 6.4 6 5) Round to the nearest
Make sure you get the grade you deserve!
How to Throw Away Marks in Maths GCSE One tragedy that only people who have marked eternal eamination papers such as GCSE will have any real idea about is the number of marks that candidates just throw
How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
Chapter 5 Resource Masters
Chapter Resource Masters New York, New York Columbus, Ohio Woodland Hills, California Peoria, Illinois StudentWorks TM This CD-ROM includes the entire Student Edition along with the Study Guide, Practice,
CSU Fresno Problem Solving Session. Geometry, 17 March 2012
CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news
D.3. Angles and Degree Measure. Review of Trigonometric Functions
APPENDIX D Precalculus Review D7 SECTION D. Review of Trigonometric Functions Angles and Degree Measure Radian Measure The Trigonometric Functions Evaluating Trigonometric Functions Solving Trigonometric
ALGEBRA 2/TRIGONOMETRY
ALGEBRA /TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA /TRIGONOMETRY Thursday, January 9, 015 9:15 a.m to 1:15 p.m., only Student Name: School Name: The possession
Area and Circumference
4.4 Area and Circumference 4.4 OBJECTIVES 1. Use p to find the circumference of a circle 2. Use p to find the area of a circle 3. Find the area of a parallelogram 4. Find the area of a triangle 5. Convert
General Physics 1. Class Goals
General Physics 1 Class Goals Develop problem solving skills Learn the basic concepts of mechanics and learn how to apply these concepts to solve problems Build on your understanding of how the world works
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:
2nd Semester Geometry Final Exam Review
Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular
Geometry EOC Practice Test #3
Class: Date: Geometry EOC Practice Test #3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which regular polyhedron has 12 petagonal faces? a. dodecahedron
2006 Geometry Form A Page 1
2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches
Trigonometry Hard Problems
Solve the problem. This problem is very difficult to understand. Let s see if we can make sense of it. Note that there are multiple interpretations of the problem and that they are all unsatisfactory.
Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: lass: ate: I: Unit 3 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. The radius, diameter, or circumference of a circle is given. Find
Exact Values of the Sine and Cosine Functions in Increments of 3 degrees
Exact Values of the Sine and Cosine Functions in Increments of 3 degrees The sine and cosine values for all angle measurements in multiples of 3 degrees can be determined exactly, represented in terms
GEOMETRY CONCEPT MAP. Suggested Sequence:
CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B. Thursday, January 29, 2004 9:15 a.m. to 12:15 p.m.
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Thursday, January 9, 004 9:15 a.m. to 1:15 p.m., only Print Your Name: Print Your School s Name: Print your name and
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
Accelerated Mathematics II Frameworks Student Edition Unit 4 Right Triangle Trigonometry
Accelerated Mathematics II Frameworks Student Edition Unit 4 Right Triangle Trigonometry 1 st Student Edition August 2009 Table of Contents Introduction..3 Eratosthenes Finds the Circumference of the Earth
/27 Intro to Geometry Review
/27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the
Page. Trigonometry Sine Law and Cosine Law. push
Trigonometry Sine Law and Cosine Law Page Trigonometry can be used to calculate the side lengths and angle measures of triangles. Triangular shapes are used in construction to create rigid structures.
Characteristics of the Four Main Geometrical Figures
Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.
Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress
Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation
Imperial Length Measurements
Unit I Measuring Length 1 Section 2.1 Imperial Length Measurements Goals Reading Fractions Reading Halves on a Measuring Tape Reading Quarters on a Measuring Tape Reading Eights on a Measuring Tape Reading
Geometry Chapter 2 Study Guide
Geometry Chapter 2 Study Guide Short Answer ( 2 Points Each) 1. (1 point) Name the Property of Equality that justifies the statement: If g = h, then. 2. (1 point) Name the Property of Congruence that justifies
Using the Quadrant. Protractor. Eye Piece. You can measure angles of incline from 0º ( horizontal ) to 90º (vertical ). Ignore measurements >90º.
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
The Dot and Cross Products
The Dot and Cross Products Two common operations involving vectors are the dot product and the cross product. Let two vectors =,, and =,, be given. The Dot Product The dot product of and is written and
Course 2 Summer Packet For students entering 8th grade in the fall
Course 2 Summer Packet For students entering 8th grade in the fall The summer packet is comprised of important topics upcoming eighth graders should know upon entering math in the fall. Please use your
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
DEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?
Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane
13. Write the decimal approximation of 9,000,001 9,000,000, rounded to three significant
æ If 3 + 4 = x, then x = 2 gold bar is a rectangular solid measuring 2 3 4 It is melted down, and three equal cubes are constructed from this gold What is the length of a side of each cube? 3 What is the
The Triangle and its Properties
THE TRINGLE ND ITS PROPERTIES 113 The Triangle and its Properties Chapter 6 6.1 INTRODUCTION triangle, you have seen, is a simple closed curve made of three line segments. It has three vertices, three