# Basic Angle Rules 5. A Short Hand Geometric Reasons. B Two Reasons. 1 Write in full the meaning of these short hand geometric reasons.

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1 si ngle Rules 5 6 Short Hnd Geometri Resons 1 Write in full the mening of these short hnd geometri resons. Short Hnd Reson Full Mening ) se s isos Δ re =. ) orr s // lines re =. ) sum s t pt = 360. d) vert opp s re =. e) o-in s // lines dd to180. f) sum s in Δ = 180. g) dj s on str line dd to 180. h) lt s // lines re =. Two Resons 1 If there is no rule linking the wnted ngle diretly to one of the given ngles, then the lultion is done in two (or more) steps, This mens you lso hve to give two (or more) geometri resons in your justifition. lulte the size of the lelled ngles. Give geometri reson (in short hnd) for eh step in your solution. ) ) 65 ) d) d Sigm Mths Workook S Geometri Resoning Sigm ulitions Ltd ISN opyright Liensing Ltd liene is required to opy ny prt of this resoure.

2 ngles in irles 4 16 ngles t the irumferene Smll Steps Rule : 1 omplete the 3 steps tken to lulte the size of ngle. Two ngles, oth on the irumferene nd stnding on the sme r, re equl. Short : s sme r = 1 lulte ngles nd y y ) Δ is right-ngled. Reson : = y = ) = 66. Reson :.. 2 lulte ngles to f. Give geometri resons. ) ngle = Reson :... =. reson : 2 =. reson : =. reson : d =. reson : 27 d D ) Δ is right-ngled. Reson : ) = Reson :.. ) ngle = Reson :... e =. reson : e f =. reson : f Sigm Mths Workook S Geometri Resoning Sigm ulitions Ltd ISN opyright Liensing Ltd liene is required to opy ny prt of this resoure.

3 31 The Rule of ythgors 2 Not the Hypotenuse ythgors Rule n e written in three different wys. 1. Strting with : 2 = Strting with : = 2 3. Strting with : = 2 1 Write down ythgors rule for this tringle in three different wys. strting with p : strting with q : strting with r : r p q Lots of rtie 1 lulte the length of the lelled sides. ) ) Write down ythgors s rule just one for eh tringle, ) the rule must strt with 2. If it is not the hypotenuse ut one of the other sides tht must e lulted, more diffiult eqution needs to e solved. lwys strt the rule with the side whih must e lulted. 9 Emple : lulte side. Working : Rule : = = = = 7.5 (2 sf) ) p q 5 2 In this question it my e the hypotenuse or one of the other sides for you to lulte. lwys write ythgors rule down, strting with the side to e lulted. Then solve the eqution nd round sensily. ) ) v w 3 omplete these lultions of side. ) 2 + = =... = ) ) = (2 sf) ) d) 0.52 y = 2 =. = 2 + = 2 =. = e) 3.4 z = (3 sf) =. 2.4 Sigm Mths Workook S Geometri Resoning Sigm ulitions Ltd ISN opyright Liensing Ltd liene is required to opy ny prt of this resoure.

4 43 pplitions of Trigonometry 4 Shpes with Stright Lines 1 Tringle is not right-ngled tringle. Show how the length of n e lulted y utting the tringle in two. Show your working m m Working with irles 1 setor hs n ngle of 75 nd hord of 5.0 m. lulte the rdius. Show your working. 5.0 m For prllellogrm re = se height. Show how you work out the re of this prllelogrm. Justify eh step. 2 Three rolls of lnk newspper re stked s shown. Eh roll hs rdius of 50 m. lulte the totl height of the stk. Show your resoning lerly. D h 6.4 m 10.2 m 125 Sigm Mths Workook S Geometri Resoning Sigm ulitions Ltd ISN opyright Liensing Ltd liene is required to opy ny prt of this resoure.

5 Geometri Resoning 4 52 Steel Frme 1 tringulr steel frme is reinfored with em, where is hlfwy side nd. Given tht = 2.0 m nd = 4.0 m, lulte... ) the distne () ) ngle ttery omprtment 1 The digrm shows ttery fitting snugly in omprtment. The ttery touhes the sides t,, R nd S. ) SR = 40. lulte SR. Give resons for your nswer. 40 S R ) Suppose SR =. Write n epression for SR in terms of. ) If SR = nd the rdius of the ttery is r mm, write n epression for the depth of the omprtment ()..... Sigm Mths Workook S Geometri Resoning Sigm ulitions Ltd ISN opyright Liensing Ltd liene is required to opy ny prt of this resoure.

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### Algebra & Functions (Maths ) opposite side Instructor: Dr. R.A.G. Seel Trigonometr Algebr & Functions (Mths 0 0) 0th Prctice Assignment hpotenuse hpotenuse side opposite side sin = opposite hpotenuse tn = opposite. Find sin, cos nd tn in 9 sin

### Integration. antidifferentiation 9 Integrtion 9A Antidifferentition 9B Integrtion of e, sin ( ) nd os ( ) 9C Integrtion reognition 9D Approimting res enlosed funtions 9E The fundmentl theorem of integrl lulus 9F Signed res 9G Further

### along the vector 5 a) Find the plane s coordinate after 1 hour. b) Find the plane s coordinate after 2 hours. c) Find the plane s coordinate L8 VECTOR EQUATIONS OF LINES HL Mth - Sntowski Vector eqution of line 1 A plne strts journey t the point (4,1) moves ech hour long the vector. ) Find the plne s coordinte fter 1 hour. b) Find the plne

### 15 - TRIGONOMETRY Page 1 ( Answers at the end of all questions ) - TRIGONOMETRY Pge P ( ) In tringle PQR, R =. If tn b c = 0, 0, then Q nd tn re the roots of the eqution = b c c = b b = c b = c [ AIEEE 00 ] ( ) In tringle ABC, let C =. If r is the inrdius nd R is the Clculus Module C Ares Integrtion Copright This puliction The Northern Alert Institute of Technolog 7. All Rights Reserved. LAST REVISED Mrch, 9 Introduction to Ares Integrtion Sttement of Prerequisite

### What else can you do? Wht else cn you do? ngle sums The size of specil ngle types lernt erlier cn e used to find unknown ngles. tht form stright line dd to 180c. lculte the size of + M, if L is stright line M + L = 180c( stright

### MATHEMATICS PART A. 1. ABC is a triangle, right angled at A. The resultant of the forces acting along AB, AC FIITJEE Solutions to AIEEE MATHEMATICS PART A. ABC is tringle, right ngled t A. The resultnt of the forces cting long AB, AC with mgnitudes AB nd respectively is the force long AD, where D is the AC foot

### Algebra Basics. Algebra Basics. Curriculum Ready ACMNA: 133, 175, 176, 177, 179. Curriulum Redy ACMNA: 33 75 76 77 79 www.mthletis.om Fill in the spes with nything you lredy know out Alger Creer Opportunities: Arhitets eletriins plumers et. use it to do importnt lultions. Give this

### Continuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom Lerning Gols Continuous Rndom Vriles Clss 5, 8.05 Jeremy Orloff nd Jonthn Bloom. Know the definition of continuous rndom vrile. 2. Know the definition of the proility density function (pdf) nd cumultive

### On the diagram below the displacement is represented by the directed line segment OA. Vectors Sclrs nd Vectors A vector is quntity tht hs mgnitude nd direction. One exmple of vector is velocity. The velocity of n oject is determined y the mgnitude(speed) nd direction of trvel. Other exmples

### Exercise sheet 6: Solutions Eerise sheet 6: Solutions Cvet emptor: These re merel etended hints, rther thn omplete solutions. 1. If grph G hs hromti numer k > 1, prove tht its verte set n e prtitioned into two nonempt sets V 1 nd

### Date Lesson Text TOPIC Homework. Solving for Obtuse Angles QUIZ ( ) More Trig Word Problems QUIZ ( ) UNIT 5 TRIGONOMETRI RTIOS Dte Lesson Text TOPI Homework pr. 4 5.1 (48) Trigonometry Review WS 5.1 # 3 5, 9 11, (1, 13)doso pr. 6 5. (49) Relted ngles omplete lesson shell & WS 5. pr. 30 5.3 (50) 5.3 5.4

### Study Guide and Intervention - Stud Guide nd Intervention with the Sme Sign The quotient of two integers with the sme sign is positive. Emple. 7 The dividend nd the divisor hve the sme sign. b. () The dividend nd divisor hve the sme

### BEGINNING ALGEBRA (ALGEBRA I) /0 BEGINNING ALGEBRA (ALGEBRA I) SAMPLE TEST PLACEMENT EXAMINATION Downlod the omplete Study Pket: http://www.glendle.edu/studypkets Students who hve tken yer of high shool lger or its equivlent with grdes

### A B= ( ) because from A to B is 3 right, 2 down. 8. Vectors nd vector nottion Questions re trgeted t the grdes indicted Remember: mgnitude mens size. The vector ( ) mens move left nd up. On Resource sheet 8. drw ccurtely nd lbel the following vectors. HW, Mth 7. CSUF. Spring 7. Nsser M. Abbsi Spring 7 Compiled on November 5, 8 t 8:8m public Contents Section.6, problem Section.6, problem Section.6, problem 5 Section.6, problem 7 6 5 Section.6, problem 5: The Definite Integrl 5.: Estimting with Finite Sums Consider moving oject its velocity (meters per second) t ny time (seconds) is given y v t = t+. Cn we use this informtion to determine the distnce