Unit 2 Review. Short Answer 1. Find the value of x. Express your answer in simplest radical form.
|
|
|
- Colin Wilkerson
- 5 years ago
- Views:
Transcription
1 Unit 2 Review Short nswer 1. Find the value of x. Express your answer in simplest radical form. 30º x 3 24 y 6 60º x 2. The size of a TV screen is given by the length of its diagonal. The screen aspect ratio is the ratio of its width to its height. The screen aspect ratio of a standard TV screen is 4:3. What are the width and height of a 27" TV screen? 5. Write the trigonometric ratio for cos X as a fraction and as a decimal rounded to the nearest hundredth. Y height 27" 15 9 X 12 Z width 3. Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain Use your calculator to find the trigonometric ratios sin 79, cos 47, and tan 77. Round to the nearest hundredth. 7. Use your calculator to find the trigonometric ratios sin 49, cos 50, and tan 45. Round to the nearest hundredth. 8. Find GH. Round to the nearest hundredth. G 4. Find the values of x and y. Express your answers in simplest radical form. F in. H
2 9. Jessie is building a ramp for loading motorcycles onto a trailer. The trailer is 2.8 feet off of the ground. To avoid making it too difficult to push a motorcycle up the ramp, Jessie decides to make the angle between the ramp and the ground 15. To the nearest hundredth of a foot, find the length of the ramp. 10. Find the sine and cosine of the acute angles in the right triangle. 1.3 cm cm cm 15. Use your calculator to find the angle measures to the nearest tenth of a degree. 16. Find to the nearest hundredth C Classify each angle in the diagram as an angle of elevation or an angle of depression. 11. Find the sine and cosine of the acute angles in the right triangle The largest Egyptian pyramid is m high. When Rowena stands far away from the pyramid, her line of sight to the top of the pyramid forms an angle of elevation of 20 with the ground. What is the horizontal distance between the center of the pyramid and Rowena? Round to the nearest meter n eagle 300 feet in the air spots its prey on the ground. The angle of depression to its prey is 15. What is the horizontal distance between the eagle and its prey? Round to the nearest foot. 12. Write cos 16 in terms of the sine. 13. Write sin 74 in terms of the cosine. 14. Use the trigonometric ratio to determine which angle of the triangle is. 20. pilot flying at an altitude of 1.8 km sights the runway directly in front of her. The angle of depression to the beginning of the runway is 31. The angle of depression to the end of the runway is 23. What is the length of the runway? Round to the nearest tenth of a kilometer.
3 Unit 2 Review nswer Section SHORT NSWER 1. NS: x = Pythagorean Theorem Substitute 3 for a, 6 for b, and x for c. Simplify. Find the positive square root. Simplify the radical. PTS: 1 DIF: 2 REF: 1af8a14a df-9c7d f0d2ea OJ: Using the Pythagorean Theorem ST: MCC9-12.G.SRT.8 LOC: MTH.C MTH.C TOP: 9-1 The Pythagorean Theorem KEY: Pythagorean Theorem side length DOK: DOK 1 2. NS: width: 21.6 in., height: 16.2 in. Let 3x be the height in inches. Then 4x is the width of the TV screen. Pythagorean Theorem Substitute 4x for a, 3x for b, and 27 for c. Multiply and combine like terms. Divide both sides by 25. in. Find the positive square root. Width: Height: in. in. PTS: 1 DIF: 2 REF: 1afadc df-9c7d f0d2ea OJ: pplication NT: NT.CCSS.MTH G.SRT.8 ST: MCC9-12.G.SRT.8 LOC: MTH.C MTH.C TOP: 9-1 The Pythagorean Theorem KEY: Pythagorean Theorem side length DOK: DOK 1 3. NS: The missing side length is 15. The side lengths form a Pythagorean triple because they are nonzero whole numbers that satisfy the equation. Pythagorean Theorem Substitute 20 for a and 25 for c. Multiply and subtract 400 from both sides. Find the positive square root.
4 The side lengths are nonzero whole numbers that satisfy the equation triple., so they form a Pythagorean PTS: 1 DIF: 1 REF: 1afd3ef df-9c7d f0d2ea OJ: Identifying Pythagorean Triples ST: MCC9-12..REI.4b LOC: MTH.C MTH.C TOP: 9-1 The Pythagorean Theorem KEY: Pythagorean Theorem side length Pythagorean triple 4. NS:, Hypotenuse Divide both sides by 2. PTS: 1 DIF: 2 REF: 1b df-9c7d f0d2ea OJ: Finding Side Lengths in a Triangle ST: MCC9-12.G.SRT.6 LOC: MTH.C MTH.C TOP: 9-2 pplying Special Right Triangles KEY: special right triangles NS: cos X = cos X = The cosine of an is. PTS: 1 DIF: 1 REF: 1bc0c06a df-9c7d f0d2ea OJ: Finding Trigonometric Ratios NT: NT.CCSS.MTH G.SRT.6 ST: MCC9-12.G.SRT.6 LOC: MTH.C MTH.C TOP: 10-1 Trigonometric Ratios KEY: trigonometric ratio trigonometry cosine 6. NS: sin 79 = 0.98, cos 47 = 0.68, tan 77 = 4.33 Make sure your calculator is in degree mode. sin 79 = 0.98, cos 47 = 0.68, tan 77 = 4.33 PTS: 1 DIF: 1 REF: 1bc349d df-9c7d f0d2ea OJ: Calculating Trigonometric Ratios NT: NT.CCSS.MTH.10.K TOP: 10-1 Trigonometric Ratios KEY: trigonometric ratio trigonometry cosine sine tangent 7. NS: sin 49 = 0.75, cos 50 = 0.64, tan 45 = 1 Make sure your calculator is in degree mode. sin 49 = 0.75, cos 50 = 0.64, tan 45 = 1 PTS: 1 DIF: 1 REF: 1bc349d df-9c7d f0d2ea
5 OJ: Calculating Trigonometric Ratios NT: NT.CCSS.MTH.10.K TOP: 10-1 Trigonometric Ratios KEY: trigonometric ratio trigonometry cosine sine tangent 8. NS: GH = in. GH is the length of the hypotenuse of the triangle. You are given FH, which is adjacent to. Since the adjacent side and hypotenuse are involved, use the cosine ratio. Write a trigonometric ratio. Substitute the given values. Multiply both sides by GH and divide by cos 35. in Simplify the expression. PTS: 1 DIF: 2 REF: 1bc df-9c7d f0d2ea OJ: Using Trigonometric Ratios to Find Lengths ST: MCC9-12.G.SRT.8 TOP: 10-1 Trigonometric Ratios KEY: trigonometric ratio trigonometry side length 9. NS: feet 2.8 ft C feet Write a trigonometric ratio. Substitute the given values. Multiply both sides by and divide by sin 15. Simplify the expression. PTS: 1 DIF: 2 REF: 1bc7e77e df-9c7d f0d2ea OJ: Problem-Solving pplication NT: NT.CCSS.MTH G.SRT.8 ST: MCC9-12.G.SRT.8 TOP: 10-1 Trigonometric Ratios KEY: trigonometric ratio trigonometry side length 10. NS: sin = ; cos = sin = ; cos = 53 53
6 PTS: 1 DIF: 1 REF: 91632d45-6ab2-11e0-9c f0d2ea OJ: 10-1-Ext.1 Finding the Sine and Cosine of cute ngles NT: NT.CCSS.MTH G.SRT.7 ST: MCC9-12.G.SRT.7 TOP: 10-1-Ext Trigonometric Ratios and Complementary ngles KEY: right triangle trigonometry sine cosine tangent 11. NS: sin = ; cos = sin = ; cos = PTS: 1 DIF: 1 REF: 91632d45-6ab2-11e0-9c f0d2ea OJ: 10-1-Ext.1 Finding the Sine and Cosine of cute ngles NT: NT.CCSS.MTH G.SRT.7 ST: MCC9-12.G.SRT.7 TOP: 10-1-Ext Trigonometric Ratios and Complementary ngles KEY: right triangle trigonometry sine cosine tangent 12. NS: sin 74 PTS: 1 DIF: 2 REF: ab2-11e0-9c f0d2ea OJ: 10-1-Ext.2 Writing Sine in Cosine Terms and Cosine in Sine Terms NT: NT.CCSS.MTH G.SRT.7 ST: MCC9-12.G.SRT.7 TOP: 10-1-Ext Trigonometric Ratios and Complementary ngles KEY: right triangle trigonometry cosine sine DOK: DOK NS: cos 16 PTS: 1 DIF: 2 REF: ab2-11e0-9c f0d2ea OJ: 10-1-Ext.2 Writing Sine in Cosine Terms and Cosine in Sine Terms NT: NT.CCSS.MTH G.SRT.7 ST: MCC9-12.G.SRT.7 TOP: 10-1-Ext Trigonometric Ratios and Complementary ngles KEY: right triangle trigonometry cosine sine DOK: DOK NS: 2 Since, 2 is. Sine is the ratio of the opposite leg to the hypotenuse. 1.2 is the length of the leg opposite. 1.3 is the length of the hypotenuse. 0.5 is the length of the leg adjacent. 1.3 is the length of the hypotenuse. PTS: 1 DIF: 2 REF: 1bc80e8e df-9c7d f0d2ea OJ: Identifying ngles from Trigonometric Ratios ST: MCC9-12.G.SRT.8 LOC: MTH.C MTH.C TOP: 10-2 Solving Right Triangles KEY: trigonometric ratio trigonometry 15. NS: = 44.4, = 72.5, = 88.5 Change your calculator to degree mode. Use the inverse trigonometric functions on your calculator to find each angle measure.
7 PTS: 1 DIF: 1 REF: 1bca49da df-9c7d f0d2ea OJ: Calculating ngle Measures from Trigonometric Ratios NT: NT.CCSS.MTH F.TF.7 ST: MCC9-12.G.SRT.8 LOC: MTH.C MTH.C MTH.C TOP: 10-2 Solving Right Triangles KEY: trigonometric ratio trigonometry inverse trigonometric ratio DOK: DOK NS: = 0.45 y the Pythagorean Theorem,. PTS: 1 DIF: 2 REF: 1bccac df-9c7d f0d2ea OJ: Solving Right Triangles ST: MCC9-12.G.SRT.8 LOC: MTH.C TOP: 10-2 Solving Right Triangles KEY: trigonometric ratio trigonometry solve right triangles 17. NS: ngles of elevation: 1, 3 ngles of depression: 2, 4 1 and 3 are formed by a horizontal line and a line of sight to a point above the line. They are angles of elevation. 2 and 4 are formed by a horizontal line and a line of sight to a point below the line. They are angles of depression. PTS: 1 DIF: 1 REF: 1bd170ee df-9c7d f0d2ea OJ: Classifying ngles of Elevation and Depression ST: MCC9-12.G.SRT.8 LOC: MTH.C MTH.C TOP: 10-3 ngles of Elevation and Depression KEY: angle of elevation angle of depression trigonometry DOK: DOK NS: 402 m m 20º x Use the side opposite and x, and the side adjacent to to write the tangent ratio. Multiply both sides by x and divide both sides by. Simplify. PTS: 1 DIF: 2 REF: 1bd197fe df-9c7d f0d2ea
8 OJ: Finding Distance by Using ngle of Elevation NT: NT.CCSS.MTH G.SRT.8 ST: MCC9-12.G.SRT.8 TOP: 10-3 ngles of Elevation and Depression KEY: angle of elevation angle of depression trigonometry 19. NS: 1,120 ft R 15º 300 ft x 15º S y the lternate Interior ngles Theorem, m. From the sketch,. So. PTS: 1 DIF: 2 REF: 1bd3d34a df-9c7d f0d2ea OJ: Finding Distance by Using ngle of Depression NT: NT.CCSS.MTH G.SRT.8 ST: MCC9-12.G.SRT.8 TOP: 10-3 ngles of Elevation and Depression KEY: angle of elevation angle of depression trigonometry 20. NS: 1.2 km 1.8 km 23 D 23 C Step 1 Draw a sketch. Let and C represent the beginning and end of the runway. Let C be the length of the runway. Step 2 Find. y the lternate Interior ngles Theorem, m. In, So Step 3 Find. y the lternate Interior ngles Theorem, m. In, So Step 4 Find. So the runway is about 1.2 km long. PTS: 1 DIF: 2 REF: 1bd3fa5a df-9c7d f0d2ea
9 OJ: pplication NT: NT.CCSS.MTH G.SRT.8 ST: MCC9-12.G.SRT.8 TOP: 10-3 ngles of Elevation and Depression KEY: angle of elevation angle of depression trigonometry
Geometry Final exam Review First Semester
Name: lass: ate: Geometry Final exam Review First Semester Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the measure of O. Then, classify the angle
8-2 Trigonometric Ratios
8-2 Trigonometric Ratios Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Write each fraction as a decimal rounded to the nearest hundredth. 1. 2. 0.67 0.29 Solve each equation. 3. 4. x = 7.25
: SINE, COSINE, & TANGENT RATIOS
Geometry Notes Packet Name: 9.2 9.4: SINE, COSINE, & TANGENT RATIOS Trigonometric Ratios A ratio of the lengths of two sides of a right triangle. For any acute angle, there is a leg Opposite the angle
Pre-AP Geometry 8-4 Study Guide: Angles of Elevation and Depression (pp ) Page! 1 of! 8
Page! 1 of! 8 Attendance Problems. 1. Identify the the pair of alternate interior angles. 2. Use a calculator to find! tan 30 to the nearest ten-thousandth. 3. Solve! tan 54 = 2500 Round your answer to
Assignment 1 and 2: Complete practice worksheet: Simplifying Radicals and check your answers
Geometry 0-03 Summary Notes Right Triangles and Trigonometry These notes are intended to be a guide and a help as you work through Chapter 8. These are not the only thing you need to read, however. Rely
Geometry Warm Up Right Triangles Day 8 Date
Geometry Warm Up Right Triangles Day 8 Name Date Questions 1 4: Use the following diagram. Round decimals to the nearest tenth. P r q Q p R 1. If PR = 12 and m R = 19, find p. 2. If m P = 58 and r = 5,
Name Date Period Notes Formal Geometry Chapter 8 Right Triangles and Trigonometry 8.1 Geometric Mean. A. Definitions: 1.
Name Date Period Notes Formal Geometry Chapter 8 Right Triangles and Trigonometry 8.1 Geometric Mean A. Definitions: 1. Geometric Mean: 2. Right Triangle Altitude Similarity Theorem: If the altitude is
15 x. Substitute. Multiply. Add. Find the positive square root.
hapter Review.1 The Pythagorean Theorem (pp. 3 70) Dynamic Solutions available at igideasmath.com Find the value of. Then tell whether the side lengths form a Pythagorean triple. c 2 = a 2 + b 2 Pythagorean
Pre-AP Geometry 8-2 Study Guide: Trigonometric Ratios (pp ) Page! 1 of! 14
Pre-AP Geometry 8-2 Study Guide: Trigonometric Ratios (pp 541-544) Page! 1 of! 14 Attendance Problems. Write each fraction as a decimal rounded to the nearest hundredths. 2 7 1.! 2.! 3 24 Solve each equation.
5-7 The Pythagorean Theorem
5-7 The Pythagorean Theorem Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Classify each triangle by its angle measures. 1. 2. acute right 3. Simplify 12 4. If a = 6, b = 7, and c = 12, find
Square Root Functions 10.1
Square Root Functions 10.1 Square Root Function contains the square root of the variable. Parent Function: f ( x) = Type of Graph: Curve Domain: x 0 Range: y 0 x Example 1 Graph f ( x) = 2 x and state
8.6 Inverse Trigonometric Ratios
www.ck12.org Chapter 8. Right Triangle Trigonometry 8.6 Inverse Trigonometric Ratios Learning Objectives Use the inverse trigonometric ratios to find an angle in a right triangle. Solve a right triangle.
Final Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question.
( Final Exam Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. is an isosceles triangle. is the longest side with length. = and =. Find. 4 x + 4 7
Geometry Right Triangles and Trigonometry
Geometry Right Triangles and Trigonometry Day Date lass Homework Th 2/16 F 2/17 N: Special Right Triangles & Pythagorean Theorem Right Triangle & Pythagorean Theorem Practice Mid-Winter reak WKS: Special
Radicals and Pythagorean Theorem Date: Per:
Math 2 Unit 7 Worksheet 1 Name: Radicals and Pythagorean Theorem Date: Per: [1-12] Simplify each radical expression. 1. 75 2. 24. 7 2 4. 10 12 5. 2 6 6. 2 15 20 7. 11 2 8. 9 2 9. 2 2 10. 5 2 11. 7 5 2
Algebra 1B. Unit 9. Algebraic Roots and Radicals. Student Reading Guide. and. Practice Problems
Name: Date: Period: Algebra 1B Unit 9 Algebraic Roots and Radicals Student Reading Guide and Practice Problems Contents Page Number Lesson 1: Simplifying Non-Perfect Square Radicands 2 Lesson 2: Radical
North Carolina Math 2 Transition Edition Unit 5 Assessment: Trigonometry
Name: Class: _ Date: _ North Carolina Math 2 Transition Edition Unit 5 Assessment: Trigonometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the
Trigonometric Functions. Copyright Cengage Learning. All rights reserved.
4 Trigonometric Functions Copyright Cengage Learning. All rights reserved. 4.3 Right Triangle Trigonometry Copyright Cengage Learning. All rights reserved. What You Should Learn Evaluate trigonometric
Geometry Midterm Review 18-19
Class: Date: Geometry Midterm Review 18-19 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of BC. a. BC = 7 c. BC = 7 b. BC = 9 d. BC =
Geometry Unit 7 - Notes Right Triangles and Trigonometry
Geometry Unit 7 - Notes Right Triangles and Trigonometry Review terms: 1) right angle ) right triangle 3) adjacent 4) Triangle Inequality Theorem Review topic: Geometric mean a = = d a d Syllabus Objective:
The graph of a proportional relation always contains the origin and has a slope equal to the constant of proportionality.
Chapter 11.1 Ratios and Rates A ratio is a comparison of two numbers, a and b, by division. The numbers a and b are called terms of the ratio. A ratio can be expressed in three different ways. 1. Word
Math 2 Trigonometry. People often use the acronym SOHCAHTOA to help remember which is which. In the triangle below: = 15
Math 2 Trigonometry 1 RATIOS OF SIDES OF A RIGHT TRIANGLE Trigonometry is all about the relationships of sides of right triangles. In order to organize these relationships, each side is named in relation
PRACTICE PROBLEMS CH 8 and Proofs
GEOM PRACTICE PROBLEMS CH 8 and Proofs 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 to
Practice Test - Chapter 4
Find the value of x. Round to the nearest tenth, if necessary. Find the measure of angle θ. Round to the nearest degree, if necessary. 1. An acute angle measure and the length of the hypotenuse are given,
Warm Up 1. What is the third angle measure in a triangle with angles measuring 65 and 43? 72
Warm Up 1. What is the third angle measure in a triangle with angles measuring 65 and 43? 72 Find each value. Round trigonometric ratios to the nearest hundredth and angle measures to the nearest degree.
Find the geometric mean between 9 and 13. Find the geometric mean between
Five-Minute Check (over Lesson 8 1) CCSS Then/Now New Vocabulary Theorem 8.4: Pythagorean Theorem Proof: Pythagorean Theorem Example 1: Find Missing Measures Using the Pythagorean Theorem Key Concept:
Ch. 2 Trigonometry Notes
First Name: Last Name: Block: Ch. 2 Trigonometry Notes 2.1 THE TANGENT RATIO 2 Ch. 2.1 HW: p. 75 #3 16, 19 4 2.2 USING THE TANGENT RATIO TO CALCULATE LENGTHS 5 Ch. 2.2 HW: p. 82 # 3 5 (a, c), #6 14 6 2.4
Let be an acute angle. Use a calculator to approximate the measure of to the nearest tenth of a degree.
Ch. 9 Test - Geo H. Let be an acute angle. Use a calculator to approximate the measure of to the nearest tenth of a degree. 1. 2. 3. a. about 58.0 c. about 1.0 b. about 49.4 d. about 32.0 a. about 52.2
Trigonometric ratios:
0 Trigonometric ratios: The six trigonometric ratios of A are: Sine Cosine Tangent sin A = opposite leg hypotenuse adjacent leg cos A = hypotenuse tan A = opposite adjacent leg leg and their inverses:
Chapter 8 Test Wednesday 3/28
Chapter 8 Test Wednesday 3/28 Warmup Pg. 487 #1-4 in the Geo book 5 minutes to finish 1 x = 4.648 x = 40.970 x = 6149.090 x = -5 What are we learning today? Pythagoras The Rule of Pythagoras Using Pythagoras
Math 1201 Review Chapter 2
Math 1201 Review hapter 2 Multiple hoice Identify the choice that best completes the statement or answers the question. 1. etermine tan Q and tan R. P 12 Q 16 R a. tan Q = 0.428571; tan R = 0.75 c. tan
Prerequisite Skills. y x =
Prerequisite Skills BLM 1 1... Solve Equations 1. Solve. 2x + 5 = 11 x 5 + 6 = 7 x 2 = 225 d) x 2 = 24 2 + 32 2 e) 60 2 + x 2 = 61 2 f) 13 2 12 2 = x 2 The Pythagorean Theorem 2. Find the measure of the
Practice Test - Chapter 4
Find the value of x. Round to the nearest tenth, if necessary. 1. An acute angle measure and the length of the hypotenuse are given, so the sine function can be used to find the length of the side opposite.
Geometry Review- Chapter Find e, and express your answer in simplest radical form.
Name: Date: Period: Geometry Review- Chapter 10 1. The diagonal of a rectangle measures 15 cm long, and the width is 10. Find the height of the rectangle and epress your answer in simplest radical form.
Unit two review (trig)
Class: Date: Unit two review (trig) Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the reference angle for 15 in standard position? A 255 C 345
Trigonometry Math 076
Trigonometry Math 076 133 Right ngle Trigonometry Trigonometry provides us with a way to relate the length of sides of a triangle to the measure of its angles. There are three important trigonometric functions
8 Right Triangle Trigonometry
www.ck12.org CHAPTER 8 Right Triangle Trigonometry Chapter Outline 8.1 THE PYTHAGOREAN THEOREM 8.2 CONVERSE OF THE PYTHAGOREAN THEOREM 8.3 USING SIMILAR RIGHT TRIANGLES 8.4 SPECIAL RIGHT TRIANGLES 8.5
Name: Period: Geometry Unit 5: Trigonometry Homework. x a = 4, b= a = 7, b = a = 6, c = a = 3, b = 7
Name: Period: Geometr Unit 5: Trigonometr Homework Section 5.1: Pthagorean Theorem Find the value of each variable or missing side. Leave answers in simplest radical form AND as a decimal rounded to the
2. What are the three other angles in standard position that have a reference angle of 54? A C B D
exam unit 2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the reference angle for 15 in standard position? A 255 C 345 B 30 D 15 2. What are
Practice with Examples
NAME -c For use with pages 527-534 Solve problems involving similar right triangles formed by the altitude drawn to the hypotenuse of a right triangle and use a geometric mean to solve problems Theorem
Math 521B Trigonometry Assignment
Math 521B Trigonometry Assignment Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the reference angle for 200 in standard position? A 100 C 20
T.4 Applications of Right Angle Trigonometry
424 section T4 T.4 Applications of Right Angle Trigonometry Solving Right Triangles Geometry of right triangles has many applications in the real world. It is often used by carpenters, surveyors, engineers,
Unit 3 Practice Test Questions Trigonometry
Unit 3 Practice Test Questions Trigonometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. How you would determine the indicated angle measure, if it
Trigonometric Ratios of Acute Angles. Evaluate reciprocal trigonometric ratios. LEARN ABOUT the Math. In ^MNP, determine the length of MN.
Trigonometric Ratios of cute ngles GOL Evaluate reciprocal trigonometric ratios. LERN BOUT the Math P From a position some distance away from the base of a tree, Monique uses a clinometer to determine
UNIT 5 SIMILARITY, RIGHT TRIANGLE TRIGONOMETRY, AND PROOF Unit Assessment
Unit 5 ircle the letter of the best answer. 1. line segment has endpoints at (, 5) and (, 11). point on the segment has a distance that is 1 of the length of the segment from endpoint (, 5). What are the
Geometry. of Right Triangles. Pythagorean Theorem. Pythagorean Theorem. Angles of Elevation and Depression Law of Sines and Law of Cosines
Geometry Pythagorean Theorem of Right Triangles Angles of Elevation and epression Law of Sines and Law of osines Pythagorean Theorem Recall that a right triangle is a triangle with a right angle. In a
Name Score Period Date. m = 2. Find the geometric mean of the two numbers. Copy and complete the statement.
Chapter 6 Review Geometry Name Score Period Date Solve the proportion. 3 5 1. = m 1 3m 4 m = 2. 12 n = n 3 n = Find the geometric mean of the two numbers. Copy and complete the statement. 7 x 7? 3. 12
2.6 Applying the Trigonometric Ratios
2.6 Applying the Trigonometric atios FOCUS Use trigonometric ratios to solve a right triangle. When we solve a triangle, we find the measures of all the angles and the lengths of all the sides. To do this
Chapter 4 Trigonometric Functions
SECTION 4.1 Special Right Triangles and Trigonometric Ratios Chapter 4 Trigonometric Functions Section 4.1: Special Right Triangles and Trigonometric Ratios Special Right Triangles Trigonometric Ratios
1. Which of the following segment lengths could be used to form a right triangle? A. 15, 36, 39 B. 3, 4, 7 C. 21, 45, 51 D.
This review is due on the day of your test: p 1 Multiple Choice. Choose the answer that best fits the solution. 1. Which of the following segment lengths could be used to form a right triangle? A. 15,
Standardized Test Practice - Cumulative, Chapters What is the value of x in the figure below?
1. What is the value of x in the figure below? 2. A baseball diamond is a square with 90-ft sides. What is the length from 3rd base to 1st base? Round to the nearest tenth. A 22.5 B 23 C 23.5 D 24 Use
Answer Key. 7.1 Tangent Ratio. Chapter 7 Trigonometry. CK-12 Geometry Honors Concepts 1. Answers
7.1 Tangent Ratio 1. Right triangles with 40 angles have two pairs of congruent angles and therefore are similar. This means that the ratio of the opposite leg to adjacent leg is constant for all 40 right
Geometry Final Exam Review
Name: Date: Period: Geometry Final Exam Review 1. Fill in the flow chart below with the properties that belong to each polygon. 2. Find the measure of each numbered angle: 3. Find the value of x 4. Calculate
Geometry. Trigonometry of Right Triangles. Slide 1 / 240. Slide 2 / 240. Slide 3 / 240
New Jersey enter for Teaching and Learning Slide 1 / 240 Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students
Part II) Practice Problems
Part II) Practice Problems 1. Calculate the value of to the nearest tenth: sin 38 80 2. Calculate the value of y to the nearest tenth: y cos 52 80 3. Calculate the value of to the nearest hundredth: tan
5.5 Special Rights. A Solidify Understanding Task
SECONDARY MATH III // MODULE 5 MODELING WITH GEOMETRY 5.5 In previous courses you have studied the Pythagorean theorem and right triangle trigonometry. Both of these mathematical tools are useful when
Name: Period: Geometry Honors Unit 5: Trigonometry Homework. x a = 4, b= a = 7, b = a = 6, c =
Name: Period: Geometr Honors Unit 5: Trigonometr Homework Section 5.1: Pthagorean Theorem Find the value of each variable or missing side. Leave answers in simplest radical form ND as a decimal rounded
Lesson 11-5: Trigonometric Ratios
Math Regents Exam Questions - Pearson Integrated Algebra Lesson 11-5 Page 1 Lesson 11-5: Trigonometric Ratios Part 1: Finding Trigonometric Ratios 1. 080414a, P.I. A.A.42 Which ratio represents cos A in
Pre-Test. Use trigonometric ratios to find the value of x. Show all your work and round your answer to the nearest tenth.
Pre-Test Name Date 1. Write the trigonometric ratios for A. Write your answers as simplified fractions. A 6 cm 10 cm sin A cos A 8 10 5 6 10 3 5 C 8 cm B tan A 8 6 3 2. Write the trigonometric ratios for
New Jersey Center for Teaching and Learning. Progressive Mathematics Initiative
Slide 1 / 240 New Jersey Center for Teaching and Learning Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students
Using the distance formula Using formulas to solve unknowns. Pythagorean Theorem. Finding Legs of Right Triangles
Math 154 Chapter 9.6: Applications of Radical Equations Objectives: Finding legs of right triangles Finding hypotenuse of right triangles Solve application problems involving right triangles Pythagorean
MATH 109 TOPIC 3 RIGHT TRIANGLE TRIGONOMETRY. 3a. Right Triangle Definitions of the Trigonometric Functions
Math 09 Ta-Right Triangle Trigonometry Review Page MTH 09 TOPIC RIGHT TRINGLE TRIGONOMETRY a. Right Triangle Definitions of the Trigonometric Functions a. Practice Problems b. 5 5 90 and 0 60 90 Triangles
PART 1: USING SCIENTIFIC CALCULATORS (50 PTS.)
Math 141 Name: MIDTERM 4 PART 1 (CHAPTERS 5 AND 6: ANALYTIC & MISC. TRIGONOMETRY) MATH 141 SPRING 2018 KUNIYUKI 150 POINTS TOTAL: 50 FOR PART 1, AND 100 FOR PART 2 Show all work, simplify as appropriate,
2014 Summer Review for Students Entering Algebra 2. TI-84 Plus Graphing Calculator is required for this course.
1. Solving Linear Equations 2. Solving Linear Systems of Equations 3. Multiplying Polynomials and Solving Quadratics 4. Writing the Equation of a Line 5. Laws of Exponents and Scientific Notation 6. Solving
sin A cos A Georgia Milestones Geometry EOC Study/Resource Guide for Students and Parents Page 73 of 182
UNIT 3: RIGHT TRIANGLE TRIGONOMETRY This unit investigates the properties of right triangles. The trigonometric ratios sine, cosine, an tangent along with the Pythagorean theorem are use to solve right
Triangles and Vectors
Chapter 3 Triangles and Vectors As was stated at the start of Chapter 1, trigonometry had its origins in the study of triangles. In fact, the word trigonometry comes from the Greek words for triangle measurement.
The Primary Trigonometric Ratios Word Problems
The Primary Trigonometric Ratios Word Problems A. Determining 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
As we know, the three basic trigonometric functions are as follows: Figure 1
Trigonometry Basic Functions As we know, the three basic trigonometric functions are as follows: sin θ = cos θ = opposite hypotenuse adjacent hypotenuse tan θ = opposite adjacent Where θ represents an
Chapter 2: Trigonometry
Chapter 2: Trigonometry Section 2.1 Chapter 2: Trigonometry Section 2.1: The Tangent Ratio Sides of a Right Triangle with Respect to a Reference Angle Given a right triangle, we generally label its sides
2. Pythagorean Theorem:
Chapter 4 Applications of Trigonometric Functions 4.1 Right triangle trigonometry; Applications 1. A triangle in which one angle is a right angle (90 0 ) is called a. The side opposite the right angle
Measurement (MM3) Similarity of Two- Dimensional Figures & Right- Angled Triangles. Name... G. Georgiou
Measurement (MM3) Similarity of Two- Dimensional Figures & Right- Angled Triangles Name... G. Georgiou 1 General Mathematics (Preliminary Course) Calculate Measurements from Scale Diagrams Solve Practical
Trigonometric Identity Practice
Trigonometric Identity Practice Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the expression that completes the equation so that it is an identity.
ALGEBRA I AND GEOMETRY SUMMER ASSIGNMENT
NAME: This packet has been designed to help you review various mathematical topics that are necessary for your success in Algebra I and/or Geometry next year, as well as PSAT/SAT/ACT. Complete all problems
Key Concept Trigonometric Ratios. length of leg opposite A length of hypotenuse. = a c. length of leg adjacent to A length of hypotenuse
8-3 Trigonometry ommon ore State Standards G-SRT..8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. lso, G-SRT..7, G-MG..1 MP 1, MP 3, MP 4, MP Objective
Show all work for full credit. Do NOT use trig to solve special right triangle problems (half credit).
Chapter 8 Retake Review 1 The length of the hypotenuse of a 30 60 90 triangle is 4. Find the perimeter. 2 What similarity statement can you write relating the three triangles in the diagram? 5 Find the
Skills Practice Skills Practice for Lesson 3.1
Skills Practice Skills Practice for Lesson.1 Name Date Get Radical or (Be)! Radicals and the Pythagorean Theorem Vocabulary Write the term that best completes each statement. 1. An expression that includes
10-1 L E S S O N M A S T E R. Name. Vocabulary. 1. Refer to the diagram at the right. Fill in the blank. a. The leg adjacent to is.
L E S S O N M S T E R Vocabular 10 Questions on SPUR Objectives 1. Refer to the diagram at the right. Fill in the blank. a. The leg adjacent to is. b. The leg opposite is. c. The hpotenuse is. C 2. Fill
Algebra II Final Exam Semester II Practice Test
Name: Class: Date: Algebra II Final Exam Semester II Practice Test 1. (10 points) A bacteria population starts at,03 and decreases at about 15% per day. Write a function representing the number of bacteria
Lesson 1: Trigonometry Angles and Quadrants
Trigonometry Lesson 1: Trigonometry Angles and Quadrants An angle of rotation can be determined by rotating a ray about its endpoint or. The starting position of the ray is the side of the angle. The position
Geo - CH11 Practice Test
Geo - H11 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Identify the secant that intersects ñ. a. c. b. l d. 2. satellite rotates 50 miles
Abs.Value Equations/Inequalities, Direct Variation, and Parallel/Perpendicular Lines - QUIZ
Abs.Value Equations/Inequalities, Direct Variation, and Parallel/Perpendicular Lines - QUIZ Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which equation
Find the perimeter of the figure named and shown. Express the perimeter in the same unit of measure that appears on the given side or sides.
Mth101 Chapter 8 HW Name Find the perimeter of the figure named and shown. Express the perimeter in the same unit of measure that appears on the given side or sides. 1) 1) Rectangle 6 in. 12 in. 12 in.
Exam Review 2 nd Semester 6-1 Operations on Functions
NAME DATE PERIOD Exam Review 2 nd Semester 6-1 Operations on Functions Find (f + g)(x), (f g)(x), (f g)(x), and (x) for each f(x) and g(x). 1. f(x) = 8x 3; g(x) = 4x + 5 2. f(x) = + x 6; g(x) = x 2 If
Geometry. Trigonometry of Right Triangles. Slide 1 / 240. Slide 2 / 240. Slide 3 / 240
New Jersey enter for Teaching and Learning Slide 1 / 240 Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students
Geometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems
Geometry Final Review Name: Per: Vocab Word Acute angle Adjacent angles Angle bisector Collinear Line Linear pair Midpoint Obtuse angle Plane Pythagorean theorem Ray Right angle Supplementary angles Complementary
NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST. Name: Date:
NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST Name: Date: Day 1 1. Determine the value of x if ΔABC is equilateral. B 7.5x 6x + 3 A Write your answer on the line. 10x 5 C What is the
Brunswick School Department Honors Geometry Unit 6: Right Triangles and Trigonometry
Understandings Questions Knowledge Vocabulary Skills Right triangles have many real-world applications. What is a right triangle? How to find the geometric mean of two numbers? What is the Pythagorean
Solving For Missing Angles Algebra 1
Name: Solving For Missing ngles lgebra 1 Date: Today we will learn how to use right triangle trigonometry to find missing angles of a right triangle. In the first eercise, though, we will review how to
MIDTERM 4 PART 1 (CHAPTERS 5 AND 6: ANALYTIC & MISC. TRIGONOMETRY) MATH 141 FALL 2018 KUNIYUKI 150 POINTS TOTAL: 47 FOR PART 1, AND 103 FOR PART
Math 141 Name: MIDTERM 4 PART 1 (CHAPTERS 5 AND 6: ANALYTIC & MISC. TRIGONOMETRY) MATH 141 FALL 018 KUNIYUKI 150 POINTS TOTAL: 47 FOR PART 1, AND 103 FOR PART Show all work, simplify as appropriate, and
During: The Pythagorean Theorem and Its converse
Before: November 1st As a warm-up, let's do the Challenge Problems from the 5.1-5.4 Quiz Yesterday 1. In Triangle ABC, centroid D is on median AM. AD = x - 3 and DM = 3x - 6. Find AM. 2. In Triangle ABC,
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 like a tree, pole, building, or cliff, we can
Name: Class: Date: Use a trigonometric ratio to determine the value of x. Round your answer to the nearest tenth.
Class: Date: Ch 9 Questions 1. Use a trigonometric ratio to determine the value of x. Round your answer to the nearest tenth. 2. 3. 4. Estimate m X to the nearest degree. 5. Katie and Matt are both flying
7.4. The Primary Trigonometric Ratios. LEARN ABOUT the Math. Connecting an angle to the ratios of the sides in a right triangle. Tip.
The Primary Trigonometric Ratios GOL Determine the values of the sine, cosine, and tangent ratios for a specific acute angle in a right triangle. LERN OUT the Math Nadia wants to know the slope of a ski
Geometry Similar Triangles & Trigonometry
1 Geometry Similar Triangles & Trigonometry 2015-10-22 www.njctl.org 2 Table of Contents Problem Solving with Similar Triangles click on the topic to go to that section Similar Triangles and Trigonometry
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. Use the appropriate identity to find the indicated function value. Rationalize the denominator,
Level 1: Simplifying (Reducing) Radicals: 1 1 = 1 = 2 2 = 4 = 3 3 = 9 = 4 4 = 16 = 5 5 = 25 = 6 6 = 36 = 7 7 = 49 =
Name Period Date Unit 5:Special Right Triangles and TrigonometryNotes Packet #1 Section 7.2/7.3: Radicals, Pythagorean Theorem, Special Right Triangles (PA) CRS NCP 24-27 Work with squares and square roots
STUDY GUIDE ANSWER KEY
STUDY GUIDE ANSWER KEY 1) (LT 4A) Graph and indicate the Vertical Asymptote, Horizontal Asymptote, Domain, -intercepts, and y- intercepts of this rational function. 3 2 + 4 Vertical Asymptote: Set the
Physics 11 Reading Booklet
In Order complete the Physics 11 Substantive Assignment, you must read and complete the self-marking exercises in this booklet. 1. Read all the information provided. 2. Complete the Practice and Self Check
Note 1: Pythagoras Theorem. The longest side is always opposite the right angle and is called the hypotenuse (H).
Trigonometry Note 1: Pythagoras Theorem The longest side is always opposite the right angle and is called the hypotenuse (H). O H x Note 1: Pythagoras Theorem In a right-angled triangle the square of the
MORE TRIGONOMETRY
MORE TRIGONOMETRY 5.1.1 5.1.3 We net introduce two more trigonometric ratios: sine and cosine. Both of them are used with acute angles of right triangles, just as the tangent ratio is. Using the diagram