# Lesson 12.1 Trigonometric Ratios

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1 Lesson 12.1 rigonometric Rtios Nme eriod Dte In Eercises 1 6, give ech nswer s frction in terms of p, q, nd r. 1. sin 2. cos 3. tn 4. sin Q 5. cos Q 6. tn Q p In Eercises 7 12, give ech nswer s deciml ccurte to three plces. 7. sin 8. cos 9. tn 10. sin R 11. cos R 12. tn R R For Eercises 13 16, solve for. Epress ech nswer ccurte to two deciml plces. 13. cos sin cos tn For Eercises 17 20, find the mesure of ech ngle to the nerest degree. 17. sin tn cos tn D 4 10 For Eercises 21 24, write trigonometric eqution you cn use to solve for the unknown vlue. hen find the vlue to one deciml plce. 21. w y 24. z q R 6 r Q 8 40 w 28 cm 14 cm cm y 55 z 91 cm For Eercises 25 32, find the vlue of ech unknown to the nerest tenth of unit f 27. t 28. h 14 cm 26 cm 9 ft 14 ft 76 f in. t 12 cm 80 h 29. Regulr pentgon with center O pothem rdius r O 6 cm Discovering Geometry rctice Your kills HER 12 75

2 Lesson 12.2 roblem olving with Right ringles Nme eriod Dte For Eercises 1 4, find the re of ech figure to the nerest squre unit. 1. re 2. re 3. shded re 4. re 13 in ft cm cm For Eercises 5 10, find ech unknown to the nerest tenth of unit. 5. re 88 cm 2 6. y ft 14 in ft 8 in. 8 in. 16 cm y 14 in. 8. dimeter 9. Right cone 10. m 24 in. 10 in cm 14 in. 13 ft 5 ft In Eercises 11 16, give ech nswer to the nerest tenth of unit. 11. ldder 7 m long stnds on level ground nd mkes 73 ngle with the ground s it rests ginst wll. How fr from the wll is the bse of the ldder? 12. monument is 116 m high nd csts shdow of 196 m. Wht is the ngle of elevtion of the sun? 13. en is pulling on toboggn rope with force of 250 newtons. he rope mkes 36 ngle with the ground. Wht force is ctully working to move the toboggn to the right? 250 N o site the top of building 1000 feet wy, you look up 24 from the horizontl. Wht is the height of the building? 15. If bot going 6 mi/hr in still wter suddenly encounters crosscurrent of 4 mi/hr, t wht ngle will the bot veer? 16. guy wire is nchored 12 feet from the bse of pole. he wire mkes 58 ngle with the ground. How long is the wire? 76 HER 12 Discovering Geometry rctice Your kills

3 Lesson 12.3 he Lw of ines Nme eriod Dte In Eercises 1 4, find the re of ech figure to the nerest squre unit. 1. re 2. re 3. re 4. Regulr hegon re 15 cm 8 ft 17 5 ft 21 cm 55 5 cm ft 8.7 m In Eercises 5 8, find ech length to the nerest centimeter. ll mesures re in centimeters. 5. m 6. n 7. p 8. q m n p q In Eercises 9 12, find the mesure of ech ngle to the nerest degree. 9. m 10. m 11. m K 12. m U m m Q m M m U R M m VU Find m nd m to the nerest degree. Find the re of to one deciml plce. 14. lrge helium blloon is tethered to the ground by two tut lines. One line is 100 feet long nd mkes n 80 ngle with the ground. he second line mkes 40 ngle with the ground. How long is the second line, to the nerest foot? How fr prt re the tethers? 15. wo ngles of tringle hve mesures 24 nd 69. he longest side of the tringle is 14.7 m. Find the lengths of the other two sides. 48 Q 26 K 78 L V cm 5.3 cm U Discovering Geometry rctice Your kills HER 12 77

4 Lesson 12.4 he Lw of osines Nme eriod Dte In Eercises 1 4, find ech length to the nerest centimeter. ll lengths re in centimeters. 1. t 2. b 3. w 4. t U O b Y W M 114 w O M In Eercises 5 7, find ech ngle mesure to the nerest degree. 5. m 6. m 7. m m m m U m m m V V U 8. circle with rdius 12 in. hs rdii drwn to the endpoints of 5 in. chord. Wht is the mesure of the centrl ngle? 9. prllelogrm hs side lengths 22.5 cm nd 47.8 cm. One ngle mesures 116. Wht is the length of the shorter digonl? 10. he digonls of prllelogrm re 60 in. nd 70 in. nd intersect t n ngle mesuring 64. Find the length of the shorter side of the prllelogrm. 11. tringulr lot fces two streets tht meet t n ngle mesuring 80. he sides of the lot fcing the streets re ech 150 feet long. Find the perimeter of the lot. 12. Find l. 25 ft l ft 48 ft In geometry gme, person with eyes closed strts t home nd wlks 5.0 m in stright line, turns 130 counterclockwise, nd wlks 7.6 m in stright line. How fr is the person from home? hrough wht counterclockwise ngle would the person turn to fce home? 78 HER 12 Discovering Geometry rctice Your kills

5 Lesson 12.5 roblem olving with rigonometry Nme eriod Dte 1. While floting down river with 2.75 mi/hr current, lici decides to swim towrd the river bnk. he cn swim 0.75 mi/hr in still wter. Wht is the ctul speed t which she moves towrd the bnk? t wht ngle will she pproch the bnk, mesured with respect to the bnk? 2. Find the mesure of ech ngle to two deciml plces. y (4, 7) c (15, 9) b (10, 0) 3. wo fire wtchtowers 8.4 km prt spot fire t the sme time. ower 1 reports the fire t 36 ngle mesure from its line of site to ower 2. ower 2 reports 68 ngle mesure between the fire nd ower 1. How fr is the fire from ech tower? 4.. Epress the cosine of ngle in terms of the sine of ngle. b. Use your nswer to prt to find cos without first finding the mesure of. Ifsin , then cos. 5. wo irplnes leve O Hre irport in hicgo t the sme time. One plne flies 280 mi/hr t bering 55. he other plne flies 350 mi/hr t bering 128. How fr prt re the two plnes fter 2 hours 15 minutes? 6. On the 240-yrd 4th hole of his municipl golf course, Lion imber hits tee shot 165 yrds but 10 off the line to the flg. he cup is t the center of circulr green with 30-foot rdius. Find the rnge of distnces Lion cn hit the bll to lnd his second shot on the green. 7. rl needs to fence her tringulr plot of lnd. he ngle between the two shorter sides mesures 83. he shortest side is 122 ft nd the longest is 215 ft. How much fencing does rl need? Wht is the re of her plot of lnd? Discovering Geometry rctice Your kills HER 12 79

6 LEON 12.1 rigonometric Rtios 1. sin p r 2. cos q r 3. tn p q 4. sin Q q r 5. cos Q p r 6. tn Q q p 7. sin cos tn sin R cos R tn R m m m m D w 18.0 cm cm 23. y 76.3 cm 24. z 11.1 cm f 12.5 ft 27. t 11.9 in. 28. h 34.0 cm 29. pothem 4.1 cm, rdius 5.1 cm LEON 12.2 roblem olving with Right ringles 1. re 2.14 cm 2 2. re 325 ft 2 3. shded re 36 cm 2 4. re 109 in y in. 8. dimeter 20.5 cm bout 2.0 m 12. bout bout newtons 14. bout ft 15. bout bout 22.6 ft LEON 12.3 he Lw of ines 1. re 46 cm 2 2. re 24 m 2 3. re 45 ft 2 4. re 65 cm 2 5. m 14 cm 6. n 37 cm 7. p 17 cm 8. q 13 cm 9. m 66, m m 37, m Q m K 81, m M m U 139, m U 41, m VU m 81, m 40, re 12.3 cm econd line: bout 153 ft, between tethers: bout 135 ft 15. bout 6.0 m nd 13.7 m LEON 12.4 he Lw of osines 1. t 13 cm 2. b 67 cm 3. w 34 cm cm 5. m 76, m 45, m m 77, m 66, m m 46, m U 85, m V bout 43.0 cm 10. bout 34.7 in. 11. bout ft 12. l 70.7 ft 13. bout 5.8 m, 139 LEON 12.5 roblem olving with rigonometry mi/hr; bout m 50.64, m 59.70, m bout 8.0 km from ower 1, 5.1 km from ower cos 1 sin 2 b. cos bout 853 miles 6. bout ft, or 218 ft l 278 ft where l is the length of the second shot 7. bout 530 ft of fencing; bout 11,656 ft 2 LEON 13.1 he remises of Geometry 1.. Given b. Distributive property c. ubstitution property d. ubtrction property e. ddition property f. Division property 2. Flse 3. Flse M D 4. rue; erpendiculr ostulte 5. rue; trnsitive property of congruence nd definition of congruence 112 NWER Discovering Geometry rctice Your kills

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