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8.3 - 8.3 The Law of Cosines Cam 3 TWO Sidﬁiﬁ and the...

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Unformatted text preview: 8.3 The Law of Cosines Cam 3: TWO Sidﬁiﬁ and the included angle are kmwn (SAS). Case 4: Three sides are RHOWI‘] (SSS). Law of Cosines Far 21 trizmgie with a! b. (t and opposita angle—3 A. B, C, respectively. ’3’; I? " “3 m “‘1‘- ss‘ﬁ“ : {r + b" —- 2gb QUE; :5“ r».- ll % 4:1 2 b5 + at“ (a (:03 C. a sin 8) f 1 ix EC 394: 33 ‘ i i | l b (a) Angie C is acute (13) Angie C is obtuse Law of Cosines Th e RqLu-Irc of mm: Side of 5:: triangle equals the sum of the SLIUE'H'CS 0!" HM: 01: her two Sides I‘ninus Iwicc their product times thc cosine (13'1" their inciucicd anqu Solve the oblique triangles. 1. a=26,b=32,C=110° 7— 2 C4: a+lo #215 003C 9 362%?) 511—— 21 [26 )(32) Cos. HO CZ: 3363.1115‘I% : quw . l 2 | a.) A bZ:G+C—-—30\CCosI' } 3313 3152.1; ﬁchuétff—a 2 ['16)(91'£%)Cosr°> _ [331):L2é)l_(qq=éq)2: ~22. 6%)[W-bq)cos;3 (32.) 7:429? —(L1Mu)l «; Cases r-2(ze) (Lflcé 2. (1:329 5:46, 6:69 3. £726, c:3, A=70° 9)”: Kim?“— leoc COS/5r a1: a aahztwsms so - 6‘12: 2 .68 12-1 /‘”““~ nf—V ‘1 ///.: (1.7- 2 - _ 2 4. A p ane eaves airport A and travels 690 miles to airport B on a bearing ofN42°E.The plane later leaves airport B and travels to airport C 525 miles away on a bearing of Ser. Find the distance from airport A to airport C to the nearest mile. I 13 A ITIOIOI‘iZBd sallbeat leaves Naples. Florida. bound for Key West. 150 miles: away. Maintaining a constant speed of ’15 miles per hour, but encountering heavy crosswith and strong currents. the crew finds, after 4 11-01113. that the sailboat is off C(IJLITSC by 20"“. (a) How far is the sailboat from Key West at. this time? (b) Through what angle should the sailboat turn to correct its course? (Cl HOW much time has been added to the trip because of this? ( Assume that lhc speed remains at 15 miles per hour.) : CH3~5+€3 3 ﬂ ‘ ' I mag-l— @ rl—hu Sail bod iS'AClGMLLLS qfoj‘m Km} (5) I60?— 9e%.eol;—2.lqe)(éq>caslx Cxogﬂ : w°940€> LL . r- ’ ‘3 ‘ l L C! v-l Curb Q I :r lquoQ 9624' 2300‘} \$1511 DZ) ~_r—%Jr/” 1%[email protected]ﬂ-2: 3%;,« kc) (ﬂail —|0lorl LQJvul-lln Eb 4M "l‘ﬂp m hub—low; [foéﬂmhqéi En Own exlva 6 W“ 3_ wh‘ch will YQ—SLLE'B’Q Ql‘i‘jfd Zhlp‘f‘nfnulox mch ih (1m gpull ES lug—mkle 3): grand -~lt‘N S (5 : I6 E " Lllwt; t, E: U Ll mm t. : 2Q minutth ...
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