Apply the Pythagorean Theorem

 Nathan Doyle
 7 months ago
 Views:
Transcription
1 8. Apply the Pythgoren Theorem The Pythgoren theorem is nmed fter the Greek philosopher nd mthemtiin Pythgors ( B.C.E.). Although nient texts indite tht different iviliztions understood this property of right tringles, Pythgors proved tht it pplies to ll right tringles. hypotenuse the longest side of right tringle the side opposite the 90 ngle If right tringle is lelled s shown, then the re of the lrge squre drwn on the hypotenuse is, while the res of the other two squres re nd. Aording to the Pythgoren reltionship, the re of the squre drwn on the hypotenuse is equl to the sum of the res of the squres drwn on the other two sides. Pythgoren theorem in right tringle, the squre of the length of the hypotenuse is equl to the sum of the squres of the lengths of the two shorter sides Tools grid pper ruler Therefore, the lgeri model for the Pythgoren reltionship is. This is known s the Pythgoren theorem. Investigte How n you illustrte the Pythgoren theorem? Method : Use Penil nd Pper. Construt ny right tringle. Lel the sides of your tringle using three different letters.. Mesure the length of eh side of your tringle. Indite these mesures on your digrm. 3. ) Clulte the re of the squre on the hypotenuse. ) Clulte the sum of the res of the squres on the two shorter sides. ) Write the Pythgoren theorem using your side lels. 48 MHR Chpter 8
2 4. ) Clulte the squre root of your nswer to step 3). ) Compre this vlue to the length of the hypotenuse. 5. Construt ny nonright tringle. Does the Pythgoren reltionship still hold? Does the reltionship from step 4, prt ), still hold? 6. Reflet Explin how this tivity illustrtes the Pythgoren theorem. Method : Use The Geometer s Skethpd. From the Edit menu, hoose Preferenes. Clik on the Units t. Set the preision to tenths for ll three oxes. Clik on the Text t nd hek For All New Points. Clik on OK.. Use the Strightedge Tool to rete ny ABC. 3. ) To mesure ABC, selet verties A, B, nd C, in tht order. From the Mesure menu, hoose Angle. ) To mesure the length of AB, selet line segment AB. From the Mesure menu, hoose Length. Repet for line segments BC nd CA. 4. ) Drg vertex of the tringle until ABC mesures 90. ) Selet the mesure mca. From the Mesure menu, hoose Clulte. Enter mca^, y seleting mca from the Vlues dropdown menu on the lultor. ) Selet mab nd mbc. From the Mesure menu, hoose Clulte. Enter mab^ mbc^. Tools omputers The Geometer s Skethpd softwre Go to links/priniples9 nd follow the links to n intertive proof of the Pythgoren theorem. Did You Know? To rete right ngle for mesuring lnd or uilding pyrmids, the nient Egyptins tied eqully sped knots in rope. They then tied the rope into loop nd strethed it to form tringle with knot t eh vertex. The only wy this works is in the rtio 3:4:5, resulting in right tringle. 8. Apply the Pythgoren Theorem MHR 49
3 d 5. ) Selet (mab ) nd (mbc ). From the Mesure menu, hoose Clulte. Evlute (mab) (mbc) y hoosing sqrt from the Funtions pulldown menu on the lultor. ) Compre this vlue to the length of side CA. 6. Drg vertex of the tringle so tht the mesure of ABC is no longer 90. Does the Pythgoren reltionship still hold? Does the reltionship from step 5) still hold? 7. Reflet Explin how this tivity illustrtes the Pythgoren theorem. Exmple Find the Hypotenuse The dvertised size of omputer or television sreen is tully the length of the digonl of the sreen. A omputer sreen mesures 30 m y.5 m. Determine the length of its digonl. Solution In the digrm, the digonl, d, is the hypotenuse. Apply the Pythgoren theorem. d d m d d 30 m Only the positive squre root needs to e used euse d 37.5 d is length. The length of the digonl of the omputer sreen is 37.5 m. Exmple Find One of the Shorter Sides Jenn is hnging light ul. She rests 4m ldder ginst vertil wll so tht its se is.4 m from the wll. How high up the wll does the top of the ldder reh? Round your nswer to the nerest tenth of metre. 40 MHR Chpter 8
4 Solution In this se, the ldder is the hypotenuse, with length of 4 m. The unknown side length is h. Apply the Pythgoren theorem. 4.4 h 6.96 h h Sutrt.96 from oth sides h 4.04 h Tke the squre root of oth sides. 3.7 h The ldder rehes 3.7 m up the wll, to the nerest tenth of metre. 4 m.4 m h Exmple 3 Clulte the Are of Right Tringle Clulte the re of the tringulr sil on the toy silot. 8 m m Solution The formul for the re of tringle is A h. The se,, nd the height, h, must e perpendiulr to eh other. For right tringle, the se nd the height re the lengths of the two shorter sides. First, use the Pythgoren theorem to find the length of the unknown side, Sutrt 64 from oth sides Tke the squre root of oth sides. 7.5 The length of side is pproximtely 7.5 m. Now, pply the formul for the re of tringle. A h (8)(7.5) 30 I n write the re formul for tringle in different wys: A h, A h, nd A 0.5h. h Liter onnetions The perpendiulr sides of right tringle re lled the legs of the tringle. The re of the sil is pproximtely 30 m. 8. Apply the Pythgoren Theorem MHR 4
5 Key Conepts The longest side of right tringle is the hypotenuse. The Pythgoren theorem sttes tht the squre of the length of the hypotenuse is equl to the sum of the squres of the lengths of the two shorter sides. An lgeri model representing the Pythgoren theorem is, where represents the length of the hypotenuse nd nd represent the lengths of the two shorter sides. You n use the Pythgoren theorem to lulte the length of n unknown side of right tringle. You n lulte the re of right tringle y using the formul A h, with the lengths of the two shorter sides s the se,, nd the height, h. If one of these dimensions is unknown nd you know the hypotenuse, pply the Pythgoren theorem to lulte the length of the unknown side. Then, use the re formul. h Communite Your Understnding C Desrie how you n use the Pythgoren theorem to determine the length of the digonl of the squre. 5 m d 5 m C Desrie how you n use the Pythgoren theorem to determine the distne etween two points on grid. y 4 A B x C3 Desrie how you would find the re of right tringle if you knew the lengths of the hypotenuse nd one of the other two sides. 5 m 3 m 4 MHR Chpter 8
6 Prtise For help with question, see Exmple.. Clulte the length of the hypotenuse in eh tringle. Round your nswers to the nerest tenth of unit, when neessry. ) ) 6 m m 8 m ) d) 5 m 4. m 7 m 5. m For help with question, see Exmple. 5 m. Clulte the length of the unknown side in eh tringle. Round your nswers to the nerest tenth of unit, when neessry. ) ) 4 m 0 m 7 m 8 m ) d) 9.5 m 5.5 m 8. m For help with question 3, see Exmple m 3. Determine the re of eh right tringle. Round your nswers to the nerest tenth of squre unit, when neessry. ) ) 7 m m 8 m 0 m 8. Apply the Pythgoren Theorem MHR 43
7 Connet nd Apply 4. Clulte the length of eh line segment. Round nswers to the nerest tenth of unit, when neessry. ) AB ) CD ) EF y A D E B C F x 5. Wht is the length of the digonl of omputer sreen tht mesures 8 m y m? 8 m m Did You Know? Bsell ws formlly introdued s medl sport t the 99 Summer Olympis in Brelon, Spin. Cnd mde its first pperne in this event in the 004 Summer Olympis. 6. A sell dimond is squre with sides tht mesure out 7 m. How fr does the seondse plyer hve to throw the ll to get runner out t home plte? Round your nswer to the nerest metre. 7 m 7. A squre ourtyrd hs digonl pths tht re eh 4 m long. Wht is the perimeter of the ourtyrd, to the nerest metre? 8. Brook is flying kite while stnding 50 m from the se of tree t the prk. Her kite is diretly ove the 0m tree nd the 5m string is fully extended. Approximtely how fr ove the tree is her kite flying? 9. Chpter Prolem Emily hs designed tringulr flower ed for the orner of her lient s retngulr lot. The ed is fened on two sides nd Emily will use order stones for the third side. The ed mesures m nd.5 m long the fened sides. How mny order stones, 30 m in length, will Emily need to edge the flower ed?.5 m m 44 MHR Chpter 8
8 Extend 0. A rdord ox mesures 40 m y 40 m y 30 m. Clulte the length of the spe digonl, to the nerest entimetre. 30 m spe digonl 40 m 40 m. The Spider nd the Fly Prolem is lssi puzzle tht originlly ppered in n English newspper in 903. It ws posed y H.E. Dudeney. In retngulr room with dimensions 30 ft y ft y ft, spider is loted in the middle of one ft y ft wll, ft wy from the eiling. A fly is in the middle of the opposite wll ft wy from the floor. If the fly does not move, wht is the shortest distne tht the spider n rwl long the wlls, eiling, nd floor to pture the fly? Hint: Using net of the room will help you get the nswer, whih is less thn 4 ft! spider fly ft 30 ft ft. A spirl is formed with right tringles, s shown in the digrm. ) Clulte the length of the hypotenuse of eh tringle, leving your nswers in squre root form. Desrie the pttern tht results. ) Clulte the re of the spirl shown. ) Desrie how the expression for the re would hnge if the pttern ontinued. 3. Mth Contest ) The set of whole numers (5,, 3) is lled Pythgoren triple. Explin why this nme is pproprite. ) The smllest Pythgoren triple is (3, 4, 5). Investigte whether multiples of Pythgoren triple mke Pythgoren triples. ) Sustitute vlues for m nd n to investigte whether triples of the form (m n, mn, m n ) re Pythgoren triples. d) Wht re the restritions on the vlues of m nd n in prt )? d 8. Apply the Pythgoren Theorem MHR 45
The Pythagorean Theorem and Its Converse Is That Right?
The Pythgoren Theorem nd Its Converse Is Tht Right? SUGGESTED LEARNING STRATEGIES: Activting Prior Knowledge, Mrking the Text, Shred Reding, Summrize/Prphrse/Retell ACTIVITY 3.6 How did Pythgors get theorem
More informationSAMPLE EVALUATION ONLY
mesurement nd geometry topic 15 Pythgors theorem 15.1 Overview Why lern this? Pythgors ws fmous mthemtiin who lived out 2500 yers go. He is redited with eing the fi rst person to prove tht in ny rightngled
More informationSkills Practice Skills Practice for Lesson 4.1
Skills Prctice Skills Prctice for Lesson.1 Nme Dte Interior nd Exterior Angles of Tringle Tringle Sum, Exterior Angle, nd Exterior Angle Inequlity Theorems Vocbulry Write the term tht best completes ech
More informationMATHEMATICAL PRACTICES In the Solve It, you used what you know about triangles to find missing lengths. Key Concept Law of Sines
85 205 Lw of Sines ontent Stndrds G.SRT.11 Understnd nd ppl the Lw of Sines... to find unknown mesurements in right nd nonright tringles... lso G.SRT.10 Ojetives To ppl the Lw of Sines 66 ft 35 135
More informationRight Triangle Trigonometry
ONDENSED LESSON 1.1 Right Tringle Trigonometr In this lesson ou will lern out the trigonometri rtios ssoited with right tringle use trigonometri rtios to find unknown side lengths in right tringle use
More informationName Class Date SAMPLE. Complete the missing numbers in the sequences below. 753, ,982. The area of the shape is approximately cm 2
End of term: TEST A You will need penil. Yer 5 Nme Clss Dte 1 2 Complete the missing numers in the sequenes elow. 200 3926 4926 400 500 700 7926 753,982 553,982 Estimte the re of the shpe elow. The re
More information7.2 Assess Your Understanding
538 HPTER 7 pplitions of Trigonometri Funtions 7. ssess Your Understnding re You Prepred? nswers re given t the end of these exerises. If you get wrong nswer, red the pges listed in red. 1. The differene
More informationWhy? DF = 1_ EF = _ AC
Similr Tringles Then You solved proportions. (Lesson 2) Now 1Determine whether two tringles re similr. 2Find the unknown mesures of sides of two similr tringles. Why? Simon needs to mesure the height
More informationMath commonly used in the US Army Pathfinder School
Mth commonly used in the US Army Pthfinder School Pythgoren Theorem is used for solving tringles when two sides re known. In the Pthfinder Course it is used to determine the rdius of circulr drop zones
More informationLesson 12.1 Right Triangle Trigonometry
Lesson 12.1 Right Tringle Trigonometr 1. For ech of the following right tringles, find the vlues of sin, cos, tn, sin, cos, nd tn. (Write our nswers s frctions in lowest terms.) 2 15 9 10 2 12 2. Drw right
More informationGrade 6. Mathematics. Student Booklet SPRING 2011 RELEASED ASSESSMENT QUESTIONS. Record your answers on the MultipleChoice Answer Sheet.
Grde 6 Assessment of Reding, Writing nd Mthemtics, Junior Division Student Booklet Mthemtics SPRING 211 RELEASED ASSESSMENT QUESTIONS Record your nswers on the MultipleChoice Answer Sheet. Plese note:
More informationLength, Perimeter and Area
Length, Perimeter n Are Teher Book  Series Mthletis Instnt Workooks Copyright Length, Perimeter n Are  Series Contents Setion Answers (p. ) units of length trvelling fr perimeter re 9 7 5 Setion Assessment
More informationCH 34 MORE PYTHAGOREAN THEOREM AND RECTANGLES
CH 34 MORE PYTHAGOREAN THEOREM AND RECTANGLES 317 Recalling The Pythagorean Theorem a 2 + b 2 = c 2 a c 90 b The 90 angle is called the right angle of the right triangle. The other two angles of the right
More informationListening & Speaking. Grade 1. Supports. instructi GRADE. Develops oral and receptive language. 15 to 20minute daily activities
Grde 1 to Stte Correlted Stndrds GRADE Develops orl nd receptive lnguge 1 EMC 2416 15 to 20minute dily ctivities Listening & Home School Connection resources Supports t s r i F g n i Red ding E bo ok
More informationPut in simplest radical form. (No decimals)
Put in simplest radical form. (No decimals) 1. 2. 3. 4. 5. 6. 5 7. 4 8. 6 9. 5 10. 9 11. 3 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 3 28. 1 Geometry Chapter 8  Right Triangles
More informationName Date PD. Pythagorean Theorem
Name Date PD Pythagorean Theorem Vocabulary: Hypotenuse the side across from the right angle, it will be the longest side Legs are the sides adjacent to the right angle His theorem states: a b c In any
More informationChapter 10. Right Triangles
Chapter 10 Right Triangles If we looked at enough right triangles and experimented a little, we might eventually begin to notice some relationships developing. For instance, if I were to construct squares
More informationCoroutines in Propeller Assembly Language
www.prllxsemiondutor.om sles@prllxsemiondutor.om support@prllxsemiondutor.om phone: 916 632 4664 fx:916 624 8003 pplition Note oroutines in Propeller ssemly Lnguge strt: The multiore P8X32 does not require
More informationApplication of Geometric Mean
Section 81: Geometric Means SOL: None Objective: Find the geometric mean between two numbers Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse
More informationERRATA for Guide for the Development of Bicycle Facilities, 4th Edition (GBF4)
Dvid Bernhrdt, P.E., President Commissioner, Mine Deprtment of Trnsporttion Bud Wright, Executive Director 444 North Cpitol Street NW, Suite 249, Wshington, DC 20001 (202) 6245800 Fx: (202) 6245806 www.trnsporttion.org
More informationCongruence Axioms. Data Required for Solving Oblique Triangles. 1 of 8 8/6/ THE LAW OF SINES
1 of 8 8/6/2004 8.1 THE LAW OF SINES 8.1 THE LAW OF SINES Congrueny and Olique Triangles Derivation of the Law of Sines Appliations Amiguous Case Area of a Triangle Until now, our work with triangles has
More informationMath Section 4.1 Special Triangles
Math 1330  Section 4.1 Special Triangles In this section, we ll work with some special triangles before moving on to defining the six trigonometric functions. Two special triangles are 30 60 90 triangles
More information9.3 AltitudeonHypotenuse Theorems
9.3 AltitudeonHypotenuse Theorems Objectives: 1. To find the geometric mean of two numbers. 2. To find missing lengths of similar right triangles that result when an altitude is drawn to the hypotenuse
More informationbark bark bat bat Multiple Meaning Words: Kindergarten to Grade 2 More Teaching Tools at harsh sound made by a dog
the brk the brk bt bt hrsh sound mde by dog Mx, stop brking! outside cover of the trunks, brnches, nd roots of woody plnts The brk of this tree is very rough. club of wood or metl used to hit the bll in
More informationLesson 21: Special Relationships within Right Triangles Dividing into Two Similar SubTriangles
: Special Relationships within Right Triangles Dividing into Two Similar SubTriangles Learning Targets I can state that the altitude of a right triangle from the vertex of the right angle to the hypotenuse
More informationRULES OF INDOOR HOCKEY
RULES OF INDOOR HOCKEY 20072008 Rules of Indoor Hokey inluding explntions Effetive from 1 Jnury 2007 for the yers 2007 nd 2008 Copyright FIH 2006 The Interntionl Hokey Federtion Rue du Vlentin 61 CH
More informationAre You Ready? Pythagorean Theorem
SKILL Pythagorean Theorem Teahing Skill Objetive Find the length of the hypotenuse of a right triangle. Have students read the Pythagorean Theorem. Restate the theorem in words, as follows: the sum of
More informationBASKETBALL SPEED AND AGILITY
SKETLL SPEED ND GILITY Off court Speed and gility Work: ox gility Drills: cone set up 5 yards apart, read and follow description Drill 1 : (1234) Sprint around cones, make hard cuts Drill 2: 12 Sprint,
More informationBicycle wheel and swivel chair
Aim: To show conservtion of ngulr momentum. To clrify the vector chrcteristics of ngulr momentum. (In this demonstrtion especilly the direction of ngulr momentum is importnt.) Subjects: Digrm: 1Q40 (Conservtion
More informationMath3. Lesson 65 The Law of Sines The Ambiguous Case
Math3 Lesson 65 The Law of Sines The miguous Case Quiz 64: 1. Find the measure of angle θ. Ө = 33.7 2. What is the cosecant ratio for ϴ? Csc Ө = 2 5 5 3. standard position angle passes through the point
More information2014 Victorian Shooting Championship
2014 Victorin Shooting Chmpionship VPCI, in conjunction with the Stte Coches nd the Stte Umpires invite ll PFA licensed petnque plyers in the Stte of Victori to tke prt in the 2014 Victorin Shooting Chmpionship.
More informationDate: Period: Directions: Answer the following questions completely on a separate sheet of paper.
Name: Right Triangle Review Sheet Date: Period: Geometry Honors Directions: Answer the following questions completely on a separate sheet of paper. Part One: Simplify the following radicals. 1) 2) 3) 4)
More informationSpecial Right Triangles
GEOMETRY Special Right Triangles OBJECTIVE #: G.SRT.C.8 OBJECTIVE Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. *(Modeling Standard) BIG IDEA (Why is
More information5.5 Use Inequalities in a Triangle
5.5 Use Inequalities in a Triangle Goal p Find possible side lengths of a triangle. Your Notes Example 1 Relate side length and angle measure Mark the largest angle, longest side, smallest angle, and shortest
More informationParallel Lines Cut by a Transversal
Name Date Class 111 Parallel Lines Cut by a Transversal Parallel Lines Parallel Lines Cut by a Transversal A line that crosses parallel lines is a transversal. Parallel lines never meet. Eight angles
More informationAreas of Parallelograms and Triangles 71
Areas of Parallelograms and Triangles 71 Parallelogram A parallelogram is a quadrilateral where the opposite sides are congruent and parallel. A rectangle is a type of parallelogram, but we often see
More informationUnit 6  Quiz 1. Look at the pictures and write the missing letters. (5x2=10)
Unit 6  Quiz Nme & Surnme :... Stuent ID Numer :... Shool :... Clss :... Dte :... Result :... A Look t the pitures n write the missing letters. (x=0 i _ i _ r _ h g _ v kk _ e _ g B Mth the wors with
More informationA Measurement Framework for National Key Performance Measures
MINISTERIAL COUNCIL ON EDUCATION, EMPLOYMENT, TRAINING AND YOUTH AFFAIRS Performnce Mesurement nd Reporting Tskforce Working for qulity eduction outcomes A Mesurement Frmework for Ntionl Key Performnce
More informationDesign and Calibration of Submerged Open Channel Flow Measurement Structures: Part 3  Cutthroat Flumes
Uth Stte University DigitlCommons@USU Reports Uth Wter Reserch Lbortory Jnury 1967 Design nd Clibrtion of Submerged Open Chnnel Flow Mesurement Structures: Prt 3  Cutthrot Flumes Gylord V. Skogerboe M.
More informationUnit #8 Review Right Triangle Trigonometry. 1. Which of the following could represent the sides of a right triangle?
Name: Date: Unit #8 Review Right Triangle Trigonometry 1. Which of the following could represent the sides of a right triangle? (1) { 6, 8,14 } (2) {, 20, } (3) { 15, 20, } (4) {,15, 20 } 2. Which of the
More informationTOOLBANK USA, INC Form 990 (2014) Page 2
Form 99 (1) Pge Prt TOOLBANK USA, NC. 9879 Sttement of Progrm Servie Aomplishments Chek if Shedule O ontins response or note to ny line in this Prt m m m m m m m m m m m m m m m m m m m m m m m m 1 Briefly
More informationBASICS OF TRIGONOMETRY
Mathematics Revision Guides Basics of Trigonometry Page 1 of 9 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier BASICS OF TRIGONOMETRY Version: 1. Date: 0910015 Mathematics Revision
More informationPythagorean Theorem in Sports
Name Date Pythagorean Theorem in Sports Activity 1: Pythagorean Theorem in Baseball Directions: Measure the distance between each of the bases using the yard stick provided. Then convert your measurements
More informationWorking Paper: Reversal Patterns
Remember to welcome ll ides in trding. AND remember to reserve your opinion until you hve independently vlidted the ide! Working Pper: Reversl Ptterns Working Pper In this pper I wnt to review nd (hopefully)
More informationTrigonometry. terminal ray
terminal ray y Trigonometry Trigonometry is the study of triangles the relationship etween their sides and angles. Oddly enough our study of triangles egins with a irle. r 1 θ osθ P(x,y) s rθ sinθ x initial
More informationThe Pythagorean Theorem Diamond in the Rough
The Pythagorean Theorem SUGGESTED LEARNING STRATEGIES: Shared Reading, Activating Prior Knowledge, Visualization, Interactive Word Wall Cameron is a catcher trying out for the school baseball team. He
More informationComparison of Uniconazole Products on Greenhouse Crops
A Report Sumitted to Fine Americs, Inc. Comprison of Uniconzole Products on Greenhouse Crops Spring 2006 Mtthew Blnchrd, Roerto Lopez, Mike Olrich, nd Erik Runkle Michign Stte University OBJECTIVE The
More informationStudent Outcomes. Lesson Notes. Classwork. Discussion (20 minutes)
Student Outcomes Students explain a proof of the converse of the Pythagorean Theorem. Students apply the theorem and its converse to solve problems. Lesson Notes Students had their first experience with
More information8.1 The Law of Sines Congruency and Oblique Triangles Using the Law of Sines The Ambiguous Case Area of a Triangle
Chapter 8 Applications of Trigonometry 81 8.1 The Law of Sines Congruency and Oblique Triangles Using the Law of Sines The Ambiguous Case Area of a Triangle A triangle that is not a right triangle is
More informationCS 188: Artificial Intelligence Spring Announcements
CS 188: Artificil Intelligence Spring 2011 Lecture 19: Dynmic Byes Nets, Nïve Byes 4/6/2011 Pieter Aeel UC Berkeley Slides dpted from Dn Klein. Announcements W4 out, due next week Mondy P4 out, due next
More informationUnit 3 Trigonometry. 3.1 Use Trigonometry to Find Lengths
Topic : Goal : Unit 3 Trigonometry trigonometry I can use the primary trig ratios to find the lengths of sides in a right triangle 3.1 Use Trigonometry to Find Lengths In any right triangle, we name the
More informationUSA Field Hockey s Modifications to the 2017 FIH Rules of Indoor Hockey
USA Field Hokey hs estlished tht the Interntionl Hokey Federtion (FIH) will e the ultimte uthority for rules governing the sport of indoor hokey in the United Sttes. This rule ook is reprinted under the
More informationGraphic Standards Guide
Grphic Stndrds Guide YOGA LOVE RUN PEACE 2 ABOUT This Grphic Stndrds Guide covers the bsic guidelines for the Lululemon Athletic s new grphic identity. The Guide provides summry of the primry fetures nd
More informationName. STAR CITY Math / Geometry / Review: Right Triangles. Teacher Period
STAR CITY Math / Geometry / Review: Right Triangles 1. Firefighters use a 20 foot extension ladder to reach 16 feet up a building. How far from the building should they place the base of the ladder? Name
More information8.G Bird and Dog Race
8.G Bird and Dog Race Alignments to Content Standards: 8.G.B Task Doug is a dog, and his friend Bert is a bird. They live in Salt Lake City, where the streets are 1/16 miles apart and arranged in a square
More informationRightangled triangles and trigonometry
Rightangled triangles and trigonometry 5 syllabusref Strand: Applied geometry eferenceence Core topic: Elements of applied geometry In this cha 5A 5B 5C 5D 5E 5F chapter Pythagoras theorem Shadow sticks
More informationFino Installation Instructions
Fino nstlltion nstrutions #1500154 Rev C Fino nstlltion nstrutions A Light Fixture Trnsformer Qty: 0 or 1 1 C Prts Rotting Mgneti Mounts Qty: 3 or 6 2 D Fixe Mgneti Mounts Qty: 4 or 8 2 E Rotting Woo
More informationDiscovering Special Triangles Learning Task
The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still
More informationLearning Objectives Source/Example Questions
Grade and Strand Learning Objectives Source/Example Questions.ca Ascent Education: http://questions.ascenteducatio n.com.ca A tree 66 meters high casts a 44meter shadow. Find the angle of elevation of
More informationMORE 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
More informationRS γ γ. * Kevin D. Dayaratna is a doctoral candidate in Mathematical Statistics at the
The Pythgoren WonLoss Formul nd Hockey: A Sttisticl Justifiction for Using the Clssic Bsebll Formul s n Evlutive Tool in Hockey By Kevin D. Dyrtn nd Steven J. Miller * October 16, 2013 Abstrct Originlly
More information81. The Pythagorean Theorem and Its Converse. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
81 he Pythagorean heorem and Its Converse Vocabulary Review 1. Write the square and the positive square root of each number. Number Square Positive Square Root 9 81 3 1 4 1 16 1 2 Vocabulary Builder leg
More informationReef stainless steel channels
Reef stainless steel channels RETE EUTIFUL RRIER FREE THROOMS. designer stainless steel channels NEW TEHNOLOGY! Reef NNO RRIER NEW! REEFHNNEL.OM.U USTRLIN MDE THE REEF PROMISE: WITH OVER 30 YERS OF MNUFTURING
More informationLesson 3: Using the Pythagorean Theorem. The Pythagorean Theorem only applies to triangles. The Pythagorean Theorem + = Example 1
Lesson 3: Using the Pythagorean Theorem The Pythagorean Theorem only applies to triangles. The Pythagorean Theorem + = Example 1 A sailboat leaves dock and travels 6 mi due east. Then it turns 90 degrees
More information8.3 Trigonometric RatiosTangent. Geometry Mr. Peebles Spring 2013
8.3 Trigonometric RatiosTangent Geometry Mr. Peebles Spring 2013 Bell Ringer 3 5 Bell Ringer a. 3 5 3 5 = 3 5 5 5 Multiply the numerator and denominator by 5 so the denominator becomes a whole number.
More informationSmallscale observations of atypical fire spread caused by the interaction of wind, terrain and fire
Smllscle oservtions of typicl fire spred cused y the interction of wind, terrin nd fire Json J. Shrples Applied nd Industril Mthemtics Reserch Group, School of Physicl Environmentl nd Mthemticl Sciences,
More informationUnit 2: Right Triangle Trigonometry RIGHT TRIANGLE RELATIONSHIPS
Unit 2: Right Triangle Trigonometry This unit investigates the properties of right triangles. The trigonometric ratios sine, cosine, and tangent along with the Pythagorean Theorem are used to solve right
More informationAcoustic measurements of bubbles in the wake of ship model in tank
Acoustic mesurements of bubbles in the wke of ship model in tnk A. Sutin,b, A. Benilov, H.S. Roh nd Y.I. Nh c Stevens Institute of Technology, Cstle Point on Hudson, Hoboken, NJ 07030, USA b Artnn Lbortories,
More informationFunctions  Trigonometry
10. Functions  Trigonometry There are si special functions that describe the relationship between the sides of a right triangle and the angles of the triangle. We will discuss three of the functions here.
More informationABSTRACT EXPERIMENTAL METHOD AND MODEL
Proceedings of The Twelfth () Interntionl Offshore nd Polr Engineering Conference Kitkyushu, Jpn, My 31, Copyright by The Interntionl Society of Offshore nd Polr Engineers ISBN 15353 (Set); ISSN 1919
More informationAN Wireless Tower Assembly Instructions
N Wireless Tower ssembly Instructions RED THOROUGHLY EFORE SSEMLY ND ERETION Thank you for your purchase of an N Wireless Self Supporting Tower. N Wireless Towers are designed and fabricated to be highstrength,
More informationINTERNATIONAL WOMEN S CRICKET COUNCIL PLAYING CONDITIONS. Except as varied hereunder the Laws of Cricket (2000 Code 2nd Edition ) shall apply.
INTERNATIONAL WOMEN S CRICKET COUNCIL PLAYING CONDITIONS Except s vried hereunder the Lws of Cricket (2000 Code 2nd Edition  2003) shll pply. 1 Lw 1  The Plyers 1.1 Lw 1.2 Nomintion of Plyers Lw 1.2
More information13.7 Quadratic Equations and Problem Solving
13.7 Quadratic Equations and Problem Solving Learning Objectives: A. Solve problems that can be modeled by quadratic equations. Key Vocabulary: Pythagorean Theorem, right triangle, hypotenuse, leg, sum,
More informationWarm Up Find what numbers the following values are in between.
Warm Up Find what numbers the following values are in between. 1. 30 2. 14 3. 55 4. 48 Color squares on each side of the triangles with map pencils. Remember A square has 4 equal sides! Looking back at
More informationMeasuring Length. Goals. You will be able to
Measuring Length Goals You will be able to choose, use, and rename metric length measurements measure perimeters of polygons solve problems using diagrams and graphs Running in a Triathlon Racing Snails
More information1. Attach beams to different parts of the playset.
MORE WAYS + Prt No.: To uild different setups: Plese keep these instrutions for future referene s they ontin importnt informtion. Atth ems to different prts of the plyset. A A # olors: Pper Stok: Pper
More informationDeriving the Law of Cosines
Name lass Date 14. Law of osines Essential Question: How can you use the Law of osines to find measures of any triangle? Resource Locker Explore Deriving the Law of osines You learned to solve triangle
More informationDebt and Incentives in Political Campaigns *
Det nd Inentives in Politil Cmpigns * Alexei Ovthinnikov nd Philip Vlt Mrh 15, 2017 Astrt Det is signifint soure of funding of politil mpigns, with lmost hlf of ll mpigns relying on some form of det. In
More informationThermal and Functional Characterization of Starch from Argentinean Corn 1
Therml nd Funtionl Chrteriztion of Strh from Argentinen Corn 1 K. Seethrmn, 2 A. Tziotis, 3 F. Borrs, 4 P. J. White, 3,5 M. Ferrer, 4 nd J. Routti 4 ABSTRACT Cerel Chem. 78(4):379 386 Sreening essions
More informationMcAfee Application Control 6.1.0
Evlution Guie MAfee Applition Control 6.1.0 For use with epoliy Orhestrtor 4.5.0 4.6.0 COPYRIGHT Copyright 2012 MAfee, In. Do not opy without permission. TRADEMARK ATTRIBUTIONS MAfee, the MAfee logo, MAfee
More informationInground Liner Measuring Form
Inground iner Measuring Form Follow the 8 Steps and submit by email, fax or mail. QUESTINS? all 8005747665 (option 3) Measuring without entering the pool: You will be able to measure horizontally,
More informationA Universal Zombie RPG AddOn
A Universl Zombie RPG AddOn Brk Blckburn Assuming you re plying gme tht uses dice for tsk resolution, the Zombie Die cn be semlessly integrted into your gme. Zombies! Thnks to George Romero, Zombies re
More informationUnit 2. Looking for Pythagoras. Investigation 5: Using the Pythagorean Theorem: Analyzing Triangles and Circles
I can understand and apply the Pythagorean Theorem. Investigation 5 Unit 2 Looking for Pythagoras Investigation 5: Using the Pythagorean Theorem: Analyzing Triangles and Circles Lesson 1: Stopping Sneaky
More informationANNEX 1 CLASSIFICATION AND LABELLING SUMMARY TABLES
ANNEX CLASSIFICATION AND LABELLING SUMMARY TABLES ANNEX CLASSIFICATION AND LABELLING SUMMARY TABLES NOTE: The codifiction of hzrd s is further explined in Annex 3 (Section ). The hzrd re intended to be
More informationRight is Special 1: Triangles on a Grid
Each student in your group should have a different equilateral triangle. Complete the following steps: Using the centimeter grid paper, determine the length of the side of the triangle. Write the measure
More informationAn Angel Came From Heaven. (from Stories And Songs Of Jesus) heav la ba ba. en, dy, by, by, heav la ba ba. from a a a. en dy by by
2 Keybord VERSES: An And Descnt Melody n cme sid, M gel You ll An Angel Cme From ven (from Sries And Songs Of sus) INTRO: Moder n cme sid, M gel You ll cme see hve hd cme see hve hd from ( = c. 108) from
More informationHistorical trend of hourly extreme rainfall in Peninsular Malaysia
Theor Appl Climtol (2015) 120:259 285 DOI 10.1007/s0070401411458 ORIGINAL PAPER Historil tren of hourly extreme rinfll in Peninsulr Mlysi A. H. Syfrin & M. D. Zlin & L. Juneng Reeive: 9 My 2013 /Aepte:
More informationKaZoon. Kite Kit. User Guide. Cautionary and Warning Statements
KaZoon Kite Kit User Guide Cautionary and Warning Statements 56799 V0717 This kit is designed and intended for educational purposes only. Use only under the direct supervision of an adult who has read
More information1 What is Trigonometry? Finding a side Finding a side (harder) Finding an angle Opposite Hypotenuse.
Trigonometry (9) Contents 1 What is Trigonometry? 1 1.1 Finding a side................................... 2 1.2 Finding a side (harder).............................. 2 1.3 Finding an angle.................................
More informationAreas of Trapezoids, Rhombuses, and Kites. To find the area of a trapezoid, rhombus, or kite
102 Areas of Trapezoids, Rombuses, and Kites Common Core State Standards GMG.A.1 Use geometric sapes, teir measures, and teir properties to describe objects. MP 1, MP 3, MP 4, MP 6 Objective To find
More informationGRAIN PROCESSING AND BYPRODUCT INTERACTIONS AN INDUSTRY PERSPECTIVE
GRAIN PROCESSING AND BYPRODUCT INTERACTIONS AN INDUSTRY PERSPECTIVE Roert J. Cooper Cttlemen s Nutrition Servies, LLC Linoln, NE rooper@ttleservies.om INTRODUCTION The vilility of orn milling yprouts hs
More informationA 28inch ribbon was cut into four equal lengths. How long was each piece of ribbon?
Name Score Benchmark Test 1 Math Course 1 For use after Lesson 0 1. (5) A inch ribbon was cut into four equal lengths. How long was each piece of ribbon? A. 7 inches B. 7 1 inches. () In a class of students
More informationParking Lot HW? Joke of the Day: What do you call a leg that is perpendicular to a foot? Goals:
Parking Lot Joke of the Day: HW? What do you call a leg that is perpendicular to a foot? a right ankle Goals: Agenda 1 19 hw? Course Recommendations Simplify Radicals skill practice L8 2 Special Right
More informationData Compression. Lossless And Lossy Compression. Text Compression. Lossless And Lossy Compression. Lossless compression is essential.
Dt Compression Lossless And Lossy Compression Reduce the size of dt. ƒ Reduces storge spce nd hence storge cost. Compression rtio = originl dt size/compressed dt size ƒ Reduces time to retrieve nd trnsmit
More informationOVERVIEW Similarity Leads to Trigonometry G.SRT.6
OVERVIEW Similarity Leads to Trigonometry G.SRT.6 G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric
More informationPerformance Comparison of Dynamic Voltage Scaling Algorithms for Hard RealTime Systems
Performnce Comprison of Dynmic Voltge Scling Algorithms for Hrd RelTime Systems Woonseok Kim Λ Dongkun Shin y HnSem Yun y Jihong Kim y Sng Lyul Min Λ School of Computer Science nd Engineering Seoul Ntionl
More informationData Compression. Reduce the size of data. Reduces time to retrieve and transmit data. Compression ratio = original data size/compressed data size
Dt Compression Reduce the size of dt. Reduces storge spce nd hence storge cost. Compression rtio = originl dt size/compressed dt size Reduces time to retrieve nd trnsmit dt. Lossless And Lossy Compression
More informationSpecial Right Triangle Task Cards
Special Right Triangle Task Cards 454590 and 306090 Special Right Triangle Task Cards 454590 and 306090 Teachers: I have included 2 sets of task cards. The first set (slides 39) asks for the answer
More informationCarcass Gain, Efficiency, and Profitability of Steers at Extended Days on Feed
Crss Gin, Effiieny, n Profitility of Steers t Extene Dys on Fee Roert G. Bonurnt, Jim C. MDonl, Glen E. Erikson, Kte Brooks, Rik N. Funston, n Kelly Bruns Summry Steers were iniviully fe for 22 n 44 ys
More informationby Craig Cassils CD orchestrated by Dominik Hauser Performed by Pembina Trails Voices directed by Ruth Wiwchar
Songs of ee y CD orhestrted y Dominik Huser erformed y emin Trils Voies direted y Ruth Wihr CD Title ge 12 I Love This Country 2 34 Build Bridge 76 Hold on to Hope 12 78 In lers ields 1810 One World
More information