6 TRIGONOMETRY TASK 6.1 TASK 6.2. hypotenuse. opposite. adjacent. opposite. hypotenuse 34. adjacent. opposite. a f

Transcription

1 1 6 TIGONOMETY TK 6.1 In eh tringle elow, note the ngle given nd stte whether the identified side is in the orret position or not opposite djent djent 32 hypotenuse djent opposite 7. hypotenuse opposite TK 6.2 For eh tringle elow, find the sides mrked with letters, orret to 3 signifint figures. ll lengths re in m d e f g h

2 9. i j k l Trigonometry Find the lengths of Find the length of m m Find the length of KN. M N Find the length of TU m 28 m L 16 m K 73 U T TK 6.3 For eh tringle elow, find the ngles mrked, orret to 1 deiml ple. ll lengths re in m e g d 3 12 h f

3 Trigonometry 3 9. Find the ngle. 6 m 10. Find the ngle m 26 m 18 m 7 3 m 11. Find the ngle. 12. If : = 2 : 5, find the ngle. 23 m m 9 4 m 6 7 m TK 6.4 In this tsk, give eh nswer to 3 signifint figures or 1 deiml ple for ngles. 1. Find the ngle. 2. Find. 8 4 m 20 m 13 m K Find LM. 38 M 17 6 m L

4 Trigonometry 4 4. uilder wnts metl support to e inlined t n ngle of 40 to the horizontl. If the vertil height from the ottom to the top of the support is 3 8 m, wht is the length of the metl support? 5. Find the length of. 12 m 7 m wire is fixed to the ground nd tthed to the top of pole of height 9 m. If the wire on the ground is 15 m from the se of the pole, t wht ngle to the horizontl is the wire? 9 m 7. = M Find the re of tringle m 8. O is the entre of irle of rdius 6 m. If ngle O = 50, find the re of tringle O. O

5 Trigonometry 5 9. is kite. Find the length of m 5 m Find the length of. 17 m o not use lultor in this question. O is the entre of the irle. is tngent to the irle. os O = sin O = 5 13 tn O = 5 12 Find the length of. O 7 5 m

6 Trigonometry 6 TK 6.5 Give nswers in this tsk to 1 deiml ple when pproprite. 1. o Yu is stnding 90 m from the foot of flgpole. The flgpole is 11 m tll. Wht is the ngle of elevtion of the top of the flgpole from o Yu? 2. os is stnding on the top of hill looking down t her villge. The ngle of depression of the top of her house is 7. If she is 163 m higher thn the top of her house, wht is the horizontl distne of os from her house? 3. Geir is stnding on top of stle, 29 m tll. friend is stnding on the ground elow, 70 m from the se of the stle. Wht is the ngle of depression of the friend from Geir? 4. mer is pled on tle to film hurh. The ngle of elevtion from the mer to the top of flgpole on the hurh tower is 5. Using the mesurements shown, wht is the horizontl distne from the flgpole to the mer? 3 m 25 m 1 2 m 5. The ngle of elevtion of ird from n oservtion point on the ground is 6 7. If the horizontl distne of the ird from the oservtion point is 230 m, how high is the ird ove the oservtion point? 6. The ngles of elevtion of the front of two tll uildings from point is shown in the digrm opposite. Wht is the differene in the heights of the two uildings? m 107 m 7. telegrph pole stnds on line joining two points nd on the ground. The telegrph pole is 9 m tll. The ngle of depression of the top of the pole to point is 4. The ngle of depression of the top of the pole to point is 7. Wht is the horizontl distne etween nd?

7 Trigonometry 7 TK 6.6 rw n urte sle drwing of eh shpe elow using the sle shown m 2 m 4 m 6 m 8 m 4 m 9 m le: 1 m for every 3 m 4 m 4 m 2 m le: 1 m for every 2 m 3. Mke sle drwing of the front of this house using sle of 1 m for every 2 m. 2 m 5 m 2 m 2 m 6 m 4. The model of sttue is mde using sle of 1 : 40. If the sttue is 3 2 m tll, how tll is the model (give your nswer in m)? 5. prk is 5 m long on mp whose sle is 1 : Find the tul length (in km) of the prk. 6. opy nd omplete the tle elow. mp length sle rel length 7m 1:60 m 5 m 1 : 2000 m 8 m 1 : km m 1 : km m 1 : m m 1 : km 7. The distne etween two towns is 25 km. How fr prt will they e on mp of sle 1 : ? 8. pln of house is mde using sle of 1 : 30. The width of the house on the pln is 40 m. Wht is the rel width of the house? (give your nswer in metres)

8 Trigonometry 8 TK 6.7 Use lultor nd give ll nswers to 3 signifint figures when pproprite. 1. This pyrmid hs squre se of side length 9 m. VM is vertil. M is the midpoint of. Find the length of M the height VM of the pyrmid. 12 m V M 2. Find the following lengths in this uoid. L K N K M L 5 m 20 m 7 m 3. mn wlks 30 m due west from the foot of n eril mst whih is 40 m high. He then wlks 50 m north. How fr is he from the top of the mst? 4. This pyrmid hs retngulr se whih is horizontl. The vertex is diretly ove the entre of the retngulr se. The perpendiulr height of the pyrmid is 27 m. Find the re of the fe 13 m 16 m 5. uoid is suh tht its height is 1 m longer thn its width nd its length is 2 m longer thn its height. If the longest digonl in the uoid is 6 m then find the width of the uoid.

9 Trigonometry 9 TK 6.8 Use lultor nd give ll nswers to 3 signifint figures. 1. TUVW is uoid. Find V ngle VU WU d ngle WUV e W f ngle WU 14 m W T 30 m V U 17 m 2. is perpendiulr to. Find ngle d the ngle etween nd the plne 31 m 25 m 7 m V 3. This pyrmid hs retngulr se. VM is vertil. M is the midpoint of. Find M VM the ngle etween V nd the plne d ngle V M 21 m 18 m 28 m 4. This digrm represents the roof of house. is horizontl with = 10 m nd = 26 m. EF is horizontl. EF is 20 m long nd 2 m ove the horizontl plne. E nd F mke the sme ngle with. FE nd FE mke the sme ngle with. N is in the plne nd is vertilly elow E. M is the midpoint of. X is the point on suh tht the ngle NX is right ngle.

10 Trigonometry 10 E F M N X d Write down the lengths of EN nd MN. Find the ngle etween EM nd the plne. lulte the length N. Find the ngle whih the line E mkes with the plne. TK 6.9 ememer sin = or sin sin = = sin sin = sin Use lultor nd give ll nswers to 3 signifint figures m Find the vlue of eh letter in uestions 1 to m m m e 6. 7 m m 72 f m h 16 m 63 d g

11 Trigonometry In tringle KLM, KM = 6 8 m, the ngle KLM = 78 nd the ngle MKL = 34. Find the perimeter of tringle KLM. 8. Mddlestone is 28 km due north of Kenton. Howik is on ering of 137 from Mddlestone nd Howik is on ering of 067 from Kenton. Find the shortest distne from Kenton to Howik. TK 6.10 ememer re = 1 sin 2 Use lultor nd give ll nswers to 3 signifint figures when pproprite. Find the vlue of eh letter in uestions 1 to m d 5 3 m 8 2 m 7 4 m e f 6 2 m 4. In tringle, = 15 1 m, = 29 7 m nd = 19 6 m. Find the re of tringle. 5. lloon trvels 15 km on ering of 029. lloon trvels 39 km on ering of 043. How fr prt re the lloons now? On wht ering would lloon hve to trvel in order to reh the position of lloon? 6. If the re of tringle is 127 m 2, find the re of tringle. 12 m 23 m m 24 h g i m

12 Trigonometry Hnif wlks 6 km on ering of 159 then 9 km on ering of 252. On wht ering must Hnif wlk to return to his strting point nd how muh further must he wlk? TK 6.11 ememer 2 = os or os = Use lultor nd give ll nswers to 3 signifint figures m m m 23 9 m m 17 m Find the vlue of eh letter in uestions 1 to 3 9 m 4. In tringle, = 32 m, = 28 m nd = 21 m. Find the size of ngle. 5. ot sils due north for 41 km then trvels on ering of 218 for 23 km. The ot then sils k to its strting position. Find the totl distne trvelled y the ot. 6. Yo is 14 km due est of vin. Yo wlks on ering of x nd vin wlks on ering of y. They meet t more southerly point when Yo hs wlked 7 km nd vin hs wlked 10 km. Find x nd y. 7. Find the perimeter of tringle. 9 m 52 8 m m