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

Transcription

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.