Section 7.2: Area of a Triangle
|
|
|
- Bartholomew Hodges
- 6 years ago
- Views:
Transcription
1 CHAPTER 7 Trigonometric Applications to Triangles Section 7.2: Area of a Triangle Finding Areas Finding Areas Formulas for the Area of a Triangle: 600 University of Houston Department of Mathematics
2 SECTION 7.2 Area of a Triangle MATH 1330 Precalculus 601
3 CHAPTER 7 Trigonometric Applications to Triangles Example: Solution: Area of a Segment of a Circle: 602 University of Houston Department of Mathematics
4 SECTION 7.2 Area of a Triangle MATH 1330 Precalculus 603
5 CHAPTER 7 Trigonometric Applications to Triangles Example: Solution: Additional Example 1: 604 University of Houston Department of Mathematics
6 SECTION 7.2 Area of a Triangle Solution: Additional Example 2: Solution: MATH 1330 Precalculus 605
7 CHAPTER 7 Trigonometric Applications to Triangles Additional Example 3: Solution: 606 University of Houston Department of Mathematics
8 SECTION 7.2 Area of a Triangle Additional Example 4: Solution: MATH 1330 Precalculus 607
9 CHAPTER 7 Trigonometric Applications to Triangles Additional Example 5: 608 University of Houston Department of Mathematics
10 SECTION 7.2 Area of a Triangle Solution: MATH 1330 Precalculus 609
11 CHAPTER 7 Trigonometric Applications to Triangles 610 University of Houston Department of Mathematics
12 Exercise Set 7.2: Area of a Triangle 1 Use the formula A bh to find the area of each of 2 the following triangles. (You may need to find the base and/or the height first, using trigonometric ratios or the Pythagorean Theorem.) Give exact values whenever possible. Otherwise, round answers to the nearest hundredth. Note: Figures may not be drawn to scale in 57 o 1. 8 cm o 10 cm 7 m 2. 7 in In ABC below, AD BC. Use the diagram below to answer the following questions. A 3 in b h c 3. 3 ft 8 ft C D B a cm 6 cm 10 m 30 o 8 m 45 o 9. (a) Use ACD to write a trigonometric ratio that involves C, b, and h. (b) Using the equation from part (a), solve for h. (c) If a represents the base of ABC, and h represents the height, then the area K of 1 ABC is K ah. Substitute the equation 2 from part (b) into this equation to obtain a formula for the area of ABC that no longer contains h. 10. (a) Use ABD to write a trigonometric ratio that involves B, c, and h. (b) Using the equation from part (a), solve for h. (c) If a represents the base of ABC, and h represents the height, then the area K of 1 ABC is K ah. Substitute the equation 2 from part (b) into this equation to obtain a formula for the area of ABC that no longer contains h. MATH 1330 Precalculus 611
13 Exercise Set 7.2: Area of a Triangle Find the area of each of the following triangles. Give exact values whenever possible. Otherwise, round answers to the nearest hundredth. Note: Figures may not be drawn to scale cm C 50 o 8 cm 11. B 6 in 120 o 10 in A T A C 17. J cm B 53 o 4.1 m A 30 o 10 cm C M 36 o 5.6 m A 13. L m 21 o S 9 m J 8 m 45 o K Q 3.5 m 125 o R D 7 ft 12 m 135 o E 5 ft G F Answer the following. Give exact values whenever possible. Otherwise, round answers to the nearest hundredth. 19. Find the area of an isosceles triangle with legs measuring 7 inches and base angles measuring Find the area of an isosceles triangle with legs measuring 10 cm and base angles measuring 75. D 28 o 8 m O 21. Find the area of GHJ, where G 120, h 8 cm, and j 15 cm. 22. Find the area of PQR, where R 47, p 7 in, and q 10 in. 612 University of Houston Department of Mathematics
14 Exercise Set 7.2: Area of a Triangle 23. Find the area of TUV, where T 28, U 81, t 12 m, and u 6.5 m. 24. Find the area of FUN, where F 92, N 28, f 9 cm, and n 8 cm. In the following questions, the radius of circle O is given, as well as the measure of central angle AOB. Find the area of the segment of circle O bounded by AB and AB. Give exact values whenever possible. Otherwise, round answers to the nearest hundredth. 25. (a) Find all solutions to sin x 0.5 for 0 x 180. (b) If the area of RST is 20 cm 2, r 16 cm and t 5 cm, find all possible measures for S. O A B 26. (a) Find all solutions to sin x 0.2 for 0 x 180. (b) If the area of PHL is 12 m 2, p 10 m and h 6m, find all possible measures for L. 27. If the area of TRG is 37 in 2, t 8 in and g 12.5 in, find all possible measures for R. 28. If the area of PSU is 20 2 cm 2, p 4 cm and s 5 cm, find all possible measures for U. 29. A regular octagon is inscribed in a circle of radius 12 in. Find the area of the octagon. 37. Radius: 8 cm Central Angle: Radius: 7 in Central Angle: 39. Radius: 4 in Central Angle: Radius: 6 cm Central Angle: A regular hexagon is inscribed in a circle of radius 11 cm. Find the area of the hexagon. 31. A regular hexagon is circumscribed about a circle of radius 6 in. Find the area of the hexagon. 32. A regular hexagon is circumscribed about a circle of radius 10 cm. Find the area of the hexagon. 33. Find the area of an equilateral triangle with side length 4 ft. 34. Find the area of a regular hexagon with side length 10 cm. 35. Find the area of a regular decagon with side length 8 in. 36. Find the area of a regular octagon with side length 12 m. MATH 1330 Precalculus 613
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
Lesson 2B: Thales Theorem
Lesson 2B: Thales Theorem Learning Targets o I can identify radius, diameter, chords, central circles, inscribed circles and semicircles o I can explain that an ABC is a right triangle, then A, B, and
Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? A. (1,10) B. (2,7) C. (3,5) D. (4,3) E.
April 9, 01 Standards: MM1Ga, MM1G1b Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? (1,10) B. (,7) C. (,) (,) (,1). Points P, Q, R, and S lie on a line
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
Section 4.2: Radians, Arc Length, and the Area of a Sector
CHAPTER 4 Trigonometric Functions Section 4.: Radians, Arc Length, and the Area of a Sector Measure of an Angle Formulas for Arc Length and Sector Area Measure of an Angle Degree Measure: 368 SECTION 4.
MCA/GRAD Formula Review Packet
MCA/GRAD Formula Review Packet 1 2 3 4 5 6 The MCA-II / BHS 2 Math Plan GRAD Page 1 of 16 Portions Copyright 2005 by Claude Paradis 8 9 10 12 11 13 14 15 16 1 18 19 20 21 The MCA-II / BHS 2 Math Plan GRAD
CN#5 Objectives 5/11/ I will be able to describe the effect on perimeter and area when one or more dimensions of a figure are changed.
CN#5 Objectives I will be able to describe the effect on perimeter and area when one or more dimensions of a figure are changed. When the dimensions of a figure are changed proportionally, the figure will
Mathematics 5 SN TRIGONOMETRY PROBLEMS 2., which one of the following statements is TRUE?, which one of the following statements is TRUE?
Mathematics 5 SN TRIGONOMETRY PROBLEMS 1 If x 4 which one of the following statements is TRUE? A) sin x > 0 and cos x > 0 C) sin x < 0 and cos x > 0 B) sin x > 0 and cos x < 0 D) sin x < 0 and cos x
Arkansas Council of Teachers of Mathematics 2012 State Competition Geometry Exam. B. 28 (5x-41) 3 m (2x+25)
rkansas ouncil of Teachers of Mathematics 2012 State ompetition Geometry Exam For questions 1 through 25, mark your answer choice on the answer sheet provided. (Figures may not be drawn to scale.) fter
Thanks for downloading this product from Time Flies!
Thanks for downloading this product from Time Flies! I hope you enjoy using this product. Follow me at my TpT store! My Store: https://www.teacherspayteachers.com/store/time-flies 2018 Time Flies. All
Example 1: Finding angle measures: I ll do one: We ll do one together: You try one: ML and MN are tangent to circle O. Find the value of x
Ch 1: Circles 1 1 Tangent Lines 1 Chords and Arcs 1 3 Inscribed Angles 1 4 Angle Measures and Segment Lengths 1 5 Circles in the coordinate plane 1 1 Tangent Lines Focused Learning Target: I will be able
Meet #4. Math League SCASD. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets):
Math League SCASD Meet #4 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : Properties of Circles 3. Number Theory: Modular Arithmetic,
1 The six trigonometric functions
Spring 017 Nikos Apostolakis 1 The six trigonometric functions Given a right triangle, once we select one of its acute angles, we can describe the sides as O (opposite of ), A (adjacent to ), and H ().
Trigonometry. Sin θ Cos θ Tan θ Cot θ Sec θ Cosec θ. Sin = = cos = = tan = = cosec = sec = 1. cot = sin. cos. tan
Trigonometry Trigonometry is one of the most interesting chapters of Quantitative Aptitude section. Basically, it is a part of SSC and other bank exams syllabus. We will tell you the easy method to learn
Mid-Chapter Quiz: Lessons 10-1 through Refer to. 1. Name the circle. SOLUTION: The center of the circle is A. Therefore, the circle is ANSWER:
Refer to. 1. Name the circle. The center of the circle is A. Therefore, the circle is 2. Name a diameter. ; since is a chord that passes through the center, it is a diameter. 3. Name a chord that is not
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
Geometry Problem Solving Drill 07: Properties of Triangles
Geometry Problem Solving Drill 07: Properties of Triangles Question No. 1 of 10 Question 1. In ABC, m A = 44 and m C = 71. Find m B. Question #01 (A) 46 (B) 65 (C) 19 (D) 75 You thought the sum of A and
G.C.B.5: Arc Length 1
Regents Exam Questions G.C.B.5: Arc Length www.jmap.org Name: G.C.B.5: Arc Length The diagram below shows circle O with radii OA and OB. The measure of angle AOB is 0, and the length of a radius is inches.
G.C.B.5: Arc Length 1
Regents Exam Questions G.C.B.5: Arc Length 1 www.jmap.org Name: G.C.B.5: Arc Length 1 1 A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
MATH 116 Test Review sheet SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Find the complement of an angle whose measure
Math Contest, Fall 2017 BC EXAM , z =
Math Contest, Fall 017 BC EXAM 1. List x, y, z in order from smallest to largest fraction: x = 111110 111111, y = 1 3, z = 333331 333334 Consider 1 x = 1 111111, 1 y = thus 1 x > 1 z > 1 y, and so x
A. 180 B. 108 C. 360 D. 540
Part I - Multiple Choice - Circle your answer: 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C. eight D. ten 3. The sum of the interior
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
2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures three times the measure of angle A. If AC = 26, find AB.
2009 FGCU Mathematics Competition. Geometry Individual Test 1. You want to prove that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex. Which postulate/theorem
Geometry Honors Final Exam Review June 2018
Geometry Honors Final Exam Review June 2018 1. Determine whether 128 feet, 136 feet, and 245 feet can be the lengths of the sides of a triangle. 2. Casey has a 13-inch television and a 52-inch television
High School Math Contest
High School Math Contest University of South Carolina February 4th, 017 Problem 1. If (x y) = 11 and (x + y) = 169, what is xy? (a) 11 (b) 1 (c) 1 (d) 4 (e) 48 Problem. Suppose the function g(x) = f(x)
Mu Alpha Theta State 2007 Euclidean Circles
Mu Alpha Theta State 2007 Euclidean Circles 1. Joe had a bet with Mr. Federer saying that if Federer can solve the following problem in one minute, Joe would be his slave for a whole month. The problem
Chapter 7 Sect. 2. A pythagorean triple is a set of three nonzero whole numbers a, b, and c, that satisfy the equation a 2 + b 2 = c 2.
Chapter 7 Sect. 2 The well-known right triangle relationship called the Pythagorean Theorem is named for Pythagoras, a Greek mathematician who lived in the sixth century b.c. We now know that the Babylonians,
221 MATH REFRESHER session 3 SAT2015_P06.indd 221 4/23/14 11:39 AM
Math Refresher Session 3 1 Area, Perimeter, and Volume Problems Area, Perimeter, and Volume 301. Formula Problems. Here, you are given certain data about one or more geometric figures, and you are asked
1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT.
1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would prove l m? 1) 2.5 2) 4.5 3)
Lesson 12.1 Skills Practice
Lesson 12.1 Skills Practice Introduction to ircles ircle, Radius, and iameter Vocabulary efine each term in your own words. 1. circle circle is a collection of points on the same plane equidistant from
Ch 10 Review. Multiple Choice Identify the choice that best completes the statement or answers the question.
Ch 10 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In the diagram shown, the measure of ADC is a. 55 b. 70 c. 90 d. 180 2. What is the measure
Geometry Individual. AoPS Mu Alpha Theta. February 23 - March 9, 2019
AoPS Mu Alpha Theta February 2 - March 9, 2019 1 The answer choice denotes that none of these answers are correct. Tests are scored such that each correct answer is worth 4 points, each question left blank
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,
Comprehensive Mathematics Contest
Comprehensive Mathematics Contest Elon University Mathematics and Statistics Department Saturday, March 17, 2018 Multiple Choice 1. Let a and b be lengths of the major and minor axis of the ellipse given
Math 9 Chapter 8 Practice Test
Name: Class: Date: ID: A Math 9 Chapter 8 Practice Test Short Answer 1. O is the centre of this circle and point Q is a point of tangency. Determine the value of t. If necessary, give your answer to the
PRACTICE TEST 1 Math Level IC
SOLID VOLUME OTHER REFERENCE DATA Right circular cone L = cl V = volume L = lateral area r = radius c = circumference of base h = height l = slant height Sphere S = 4 r 2 V = volume r = radius S = surface
Geometry Problem Solving Drill 08: Congruent Triangles
Geometry Problem Solving Drill 08: Congruent Triangles Question No. 1 of 10 Question 1. The following triangles are congruent. What is the value of x? Question #01 (A) 13.33 (B) 10 (C) 31 (D) 18 You set
G.C.B.5: Arc Length 1
Regents Exam Questions G.C.B.5: Arc Length 1 www.jmap.org Name: G.C.B.5: Arc Length 1 1 A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian
Lesson 12.1 Skills Practice
Lesson 12.1 Skills Practice Name Date Introduction to Circles Circle, Radius, and Diameter Vocabulary Define each term in your own words. 1. circle 2. center of a circle 3. radius of a circle 4. diameter
Precalculus Summer Assignment 2015
Precalculus Summer Assignment 2015 The following packet contains topics and definitions that you will be required to know in order to succeed in CP Pre-calculus this year. You are advised to be familiar
To find the areas of circles, sectors, and segments of circles. Getting Ready! Length of Side, s. Number of Sides, n
07 Areas of Circles and Sectors Mathematics Florida Standards MAFS.912.G-C.2.5 Derive.,.the formula for the area of a sector. MP1. MP 3, MP4, MP6, MP 8 Objective To find the areas of circles, sectors,
Math 9 Unit 8: Circle Geometry Pre-Exam Practice
Math 9 Unit 8: Circle Geometry Pre-Exam Practice Name: 1. A Ruppell s Griffon Vulture holds the record for the bird with the highest documented flight altitude. It was spotted at a height of about 11 km
10.5 Areas of Circles and Sectors
10.5. Areas of Circles and Sectors www.ck12.org 10.5 Areas of Circles and Sectors Learning Objectives Find the area of circles, sectors, and segments. Review Queue Find the area of the shaded region in
1 What is the solution of the system of equations graphed below? y = 2x + 1
1 What is the solution of the system of equations graphed below? y = 2x + 1 3 As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A'B'C'D'E'F'. y = x 2 + 2x
Geometry Honors Homework
Geometry Honors Homework pg. 1 12-1 Practice Form G Tangent Lines Algebra Assume that lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x? 1. 2. 3. The circle
Answers. Investigation 4. ACE Assignment Choices. Applications. The number under the square root sign increases by 1 for every new triangle.
Answers Investigation 4 ACE Assignment Choices Problem 4. Core, Other Connections 6 Problem 4. Core, 4, Other Applications 6 ; Connections 7, 6, 7; Extensions 8 46; unassigned choices from earlier problems
Due to the detail of some problems, print the contests using a normal or high quality setting.
General Contest Guidelines: Keep the contests secure. Discussion about contest questions is not permitted prior to giving the contest. Due to the detail of some problems, print the contests using a normal
GEOMETRY ADDITIONAL PRACTICE ITEMS
GEOMETRY ADDITIONAL PRACTICE ITEMS Geometry Additional Practice Items This section has two parts. The first part is a set of 4 sample items for Geometry. The second part contains a table that shows for
A shape which can be divided by a straight line, so that each part is the mirror image of the other has reflective symmetry.
SYMMETRY There are two kinds of symmetry: a) reflective symmetry b) rotational symmetry a) Reflective Symmetry A shape which can be divided by a straight line, so that each part is the image of the other
TENTH YEAR MATHEMATICS
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION TENTH YEAR MATHEMATICS Tuesday, June 16,1987-1:15 to 4:15 p.m., only The last page of the booklet is the answer sheet. Fold the last
Geometry Cumulative Review
Geometry Cumulative Review Name 1. Find a pattern for the sequence. Use the pattern to show the next term. 1, 3, 9, 27,... A. 81 B. 45 C. 41 D. 36 2. If EG = 42, find the value of y. A. 5 B. C. 6 D. 7
Precalculus A - Final Exam Review Fall, 2014
Name: Precalculus A - Final Exam Review Fall, 2014 Period: Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 1) 85 2) -166 3) 3 Convert the radian
Geometry M1: Unit 3 Practice Exam
Class: Date: Geometry M1: Unit 3 Practice Exam Short Answer 1. What is the value of x? 2. What is the value of x? 3. What is the value of x? 1 4. Find the value of x. The diagram is not to scale. Given:
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
Exercise Set 6.2: Double-Angle and Half-Angle Formulas
Exercise Set : Double-Angle and Half-Angle Formulas Answer the following π 1 (a Evaluate sin π (b Evaluate π π (c Is sin = (d Graph f ( x = sin ( x and g ( x = sin ( x on the same set of axes (e Is sin
The Theorem of Pythagoras
CONDENSED LESSON 9.1 The Theorem of Pythagoras In this lesson you will Learn about the Pythagorean Theorem, which states the relationship between the lengths of the legs and the length of the hypotenuse
0615geo. Geometry CCSS Regents Exam In the diagram below, congruent figures 1, 2, and 3 are drawn.
0615geo 1 Which object is formed when right triangle RST shown below is rotated around leg RS? 4 In the diagram below, congruent figures 1, 2, and 3 are drawn. 1) a pyramid with a square base 2) an isosceles
GEOMETRY (Common Core)
GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Tuesday, June 2, 2015 1:15 to 4:15 p.m., only Student Name: School Name: The possession
Geometry: Hutschenreuter Semester II. Select the best answer for each question. Show expected work. MAKE A SUPPORTING SKETCH!
Geometry: Hutschenreuter Semester II Review B Name Period Date Select the best answer for each question. Show expected work. MAKE A SUPPORTING SKETCH! 1. A parallelogram has a diagonal of 41 cm and side
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
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
Summer Work for students entering PreCalculus
Summer Work for students entering PreCalculus Name Directions: The following packet represent a review of topics you learned in Algebra 1, Geometry, and Algebra 2. Complete your summer packet on separate
0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.
Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would
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
Geometry Honors Exam. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Class: Date: Geometry Honors Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the conclusion of the following conditional? A number is divisible
Summer Work for students entering PreCalculus
Summer Work for students entering PreCalculus Name Directions: The following packet represent a review of topics you learned in Algebra 1, Geometry, and Algebra 2. Complete your summer packet on separate
2016 State Mathematics Contest Geometry Test
2016 State Mathematics Contest Geometry Test In each of the following, choose the BEST answer and record your choice on the answer sheet provided. To ensure correct scoring, be sure to make all erasures
Classwork. Opening Exercises 1 2. Note: Figures not drawn to scale. 1. Determine the volume for each figure below.
Classwork Opening Exercises 1 2 Note: Figures not drawn to scale. 1. Determine the volume for each figure below. a. Write an expression that shows volume in terms of the area of the base,, and the height
Geometry. A. Right Triangle. Legs of a right triangle : a, b. Hypotenuse : c. Altitude : h. Medians : m a, m b, m c. Angles :,
Geometry A. Right Triangle Legs of a right triangle : a, b Hypotenuse : c Altitude : h Medians : m a, m b, m c Angles :, Radius of circumscribed circle : R Radius of inscribed circle : r Area : S 1. +
Final Exam Review Packet
Final Exam Review Packet 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 scale. 6 8 a.
Log1 Contest Round 2 Theta Geometry
008 009 Log Contest Round Theta Geometry Name: Leave answers in terms of π. Non-integer rational numbers should be given as a reduced fraction. Units are not needed. 4 points each What is the perimeter
How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots
. Approximating Square Roots How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots Work with a partner. Archimedes was a Greek mathematician,
Exercise Set 4.1: Special Right Triangles and Trigonometric Ratios
Eercise Set.1: Special Right Triangles and Trigonometric Ratios Answer the following. 9. 1. If two sides of a triangle are congruent, then the opposite those sides are also congruent. 2. If two angles
Name: GEOMETRY: EXAM (A) A B C D E F G H D E. 1. How many non collinear points determine a plane?
GMTRY: XM () Name: 1. How many non collinear points determine a plane? ) none ) one ) two ) three 2. How many edges does a heagonal prism have? ) 6 ) 12 ) 18 ) 2. Name the intersection of planes Q and
DISCOVERING THE PYTHAGOREAN IDENTITIES LEARNING TASK:
Name: Class Period: DISCOVERING THE PYTHAGOREAN IDENTITIES LEARNING TASK: An identity is an equation that is valid for all values of the variable for which the epressions in the equation are defined. You
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
Unit 10 Geometry Circles. NAME Period
Unit 10 Geometry Circles NAME Period 1 Geometry Chapter 10 Circles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (10-1) Circles and Circumference
Statistics. To find the increasing cumulative frequency, we start with the first
Statistics Relative frequency = frequency total Relative frequency in% = freq total x100 To find the increasing cumulative frequency, we start with the first frequency the same, then add the frequency
CP Geometry Final Exam Review Packet
CP Geometry Final Exam Review Packet 016-017 This packet reviews the basic concepts that you learned in each of the units taught this semester that will be assessed on the final exam. You should complete
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, June 19, :15 a.m. to 12:15 p.m.
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 19, 2013 9:15 a.m. to 12:15 p.m., only SAMPLE RESPONSE SET Table of Contents Practice Papers Question 29.......................
LESSON 11 PRACTICE PROBLEMS
LESSON 11 PRACTICE PROBLEMS 1. a. Determine the volume of each of the figures shown below. Round your answers to the nearest integer and include appropriate units of b. Determine the volume of each of
9. AD = 7; By the Parallelogram Opposite Sides Theorem (Thm. 7.3), AD = BC. 10. AE = 7; By the Parallelogram Diagonals Theorem (Thm. 7.6), AE = EC.
3. Sample answer: Solve 5x = 3x + 1; opposite sides of a parallelogram are congruent; es; You could start b setting the two parts of either diagonal equal to each other b the Parallelogram Diagonals Theorem
Group/In-Class Exercises 8/18/09 g0401larson8etrig.tst 4.1 Radian and Degree Measure
Group/In-Class Exercises 8/8/09 g040larson8etrig.tst 4. Radian and Degree Measure Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The given angle
FLEX Mathematics Introduction to Trigonometry. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
FLEX Mathematics Introduction to Trigonometry Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. 1) 8 tan 0 + 3 csc 20
2012 GCSE Maths Tutor All Rights Reserved
2012 GCSE Maths Tutor All Rights Reserved www.gcsemathstutor.com This book is under copyright to GCSE Maths Tutor. However, it may be distributed freely provided it is not sold for profit. Contents angles
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Wednesday, August 16, :30 to 11:30 a.m.
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Wednesday, August 16, 000 8:30 to 11:30 a.m., only Notice... Scientific
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
Chapter 10 Worksheet 1 Name: Honors Accelerated Geometry Hour:
hapter 10 Worksheet 1 Name: Honors ccelerated Geometry Hour: For 1-15, find the measure of angle in each of the following diagrams. 1. 2.. 258 84 140 40 4. 5. 6. 2 y 80 y 72 7. 8. 9. 50 X 40 140 4 y 10.
VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)
BY:Prof. RAHUL MISHRA Class :- X QNo. VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) CIRCLES Subject :- Maths General Instructions Questions M:9999907099,9818932244 1 In the adjoining figures, PQ
Quarterly Assessment 2 STUDY GUIDE. Name: Date: Per: 1. The two triangle shaped rooms are congruent. Find the missing side lengths and angle measures.
Quarterly ssessment 2 STUDY GUIDE Name: Date: Per: 1. The two triangle shaped rooms are congruent. Find the missing side lengths and angle measures. 48 o h 8 ft r 10.5 ft u 6ft s c 42 o a. c = 8 ft r =
17. The length of a diagonal of a square is 16 inches. What is its perimeter? a. 8 2 in. b in. c in. d in. e in.
Geometry 2 nd Semester Final Review Name: 1. Pentagon FGHIJ pentagon. 2. Find the scale factor of FGHIJ to KLMNO. 3. Find x. 4. Find y. 5. Find z. 6. Find the scale factor of ABCD to EFGD. 7. Find the
Practice Test Student Answer Document
Practice Test Student Answer Document Record your answers by coloring in the appropriate bubble for the best answer to each question. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Do not open your test until instructed to do so!
Fifth Annual Columbus State Calculus Contest-Precalculus Test Sponsored by The Columbus State University Department of Mathematics April 1 th, 017 ************************* The Columbus State University
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
#1 Elementary #2 Elementary #3 Elementary #4 Elementary #5 Elementary 2013
#1 Elementary 2013 Line l has equation 3x 2y = 5. Line m intersects l when x = 3. Suppose (1, 4) lies on m. Find the x-coordinate of the point P(x, 3) that also lies on m. #2 Elementary 2013 A rectangular
LLT Education Services
8. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. (a) 4 cm (b) 3 cm (c) 6 cm (d) 5 cm 9. From a point P, 10 cm away from the
Transforming to a New Level!
Lesson 1.1 Skills Practice Name Date Transforming to a New Level! Using Transformations to Determine Perimeter and Area Problem Set Translate each given rectangle or square such that one verte of the image
HONORS GEOMETRY SUMMER REVIEW PACKET (2012)
HONORS GEOMETRY SUMMER REVIEW PACKET (01) The problems in this packet are designed to help you review topics from previous mathematics courses that are important to your success in Honors Geometry. Please
Circles Unit Test. Secondary Math II
Circles Unit Test Secondary Math II 1. Which pair of circles described are congruent to each other? Circle M has a radius of 6 m; Circle N has a diameter of 10 m. Circle J has a circumference of in; Circle