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13.6The Law of Cosines807The Law of Cosines SINGTHEAWOF\b\t\n \b\n\f\r\b\n\t\r\b\f\n\f\b\f\t\n\b\t\r\b\t\r\b\n\b\b\f\b\f\b\b\t\t\f\r\b\n\n\b\f\b\f\b\f\f\t\n\b \r\b$\b\t \f\t\n\b\r\f\t\b\f\n\t\n\b\r\b\t\nWrite law of cosines.Simplify.'(")Take square root.+\n\n ,\t\r\r\n\b\b\f\b\f\t\t\b\t\r\b \t\f\b\n\b\r\f\t\b\f\n\b\r\f\t\b\f\n\t\f\b\t\t\r\bWrite law of sines.Simplify.\t\t\n\b\n\t\r\b\f\r\r\f' "-#&!"#&*".# (!.# EXAMPLE 1 \b\t\n \b GOAL1 Use HeronÕsTo solve Whyyou should learn it GOAL2 GOAL1 you should learn 13.6 REALLIFEREALLIFEABCba 12c 16 38 \b\t\n \f\n\r\r\t\b \r\n\r\b\b \b\b \b LAW OF COSINES ABCabc \b\t\n For a derivation of STUDENTHELP Trigonometric Ratios and Functions \r\b/\f\n\t\n\b\t\r\b00\f\n\b\n\b\r\t\b\f\n\f\b 1\f\t\n\b\r\f\t\b\f \t\n\b21\f\t\n\b\t\b\f\b\f\t\b\t\n\t \t\t\n\b3\b\f\b+\f\b\n\b\r\f\t\b\f\n\tWrite law of sines.\f\t "\f\tSimplify./\t\r\r \t\t\n\b3\b\f\b\t\r\b 4\b0\n\b5\f3\t\t\f\n\r\r\b\r\f* \b\b\n33\b0\r\n\b4\b\f\n\t\b\b\n\b\b\t\n\b\f\b\f\f -\b\b\n6\f\n\b0\n\b5\f3\t3\f\n\f\b7$\b\t 3\t8\t\n\f\n\t\r\b ,\t\t\r\b\n3\b0\r\n\b/3\n\b\b\t\t3\n\t ,\t\n\n9 * \t -1\f\t\n\b\r\f\t\b\f \t\f\r\bWrite law of cosines.Simplify.Take square root.Simplify.4\b\f\n\t\b\b\n\b\b\t\n\b0\n\b5\f3\t\t\f\n\f\b\f\n* \b\b\n EXAMPLE 3 EXAMPLE 2 REALLIFEREALLIFE Softball ABCb 18 ftc 13 fta 8 ft 60 ft60 ft STUDENTHELP \f\b\rThis way, when you usebetween 0¡and 90¡. 13.6The Law of Cosines809 4\b\r\f\t\b\f\t\b\f\b\n\b\f\n\r\f\n\b\r\r\t3\r\n\b\b\n\t\r\b4\f3\r\f\b\n\b\n\n\b:\b\b,3\n\b3\n\t6\b\t -- Finding the Area of a Triangle$\b\t \t\t\n\b\f\b30\b3\b\n\b+\f\b6\b\t5\f3\r\n\t\n\b\b Finding the Volume of a Building$\r\t\b\b\t\n\n\b\n/\t\n\b\r3\b\n\b\r\t$\b\t \t\t\n\b\b\n\b\f\b4\b\f\b30\b3\b\n\b\n\b\f\b\f24\t\n\b\r3\b 3\r\n0\r \n\f\b \n\b\r\t5\f\b\n2?\r3\b \b\f\b6\b\n' " --)- !- ---\b\b\n EXAMPLE 5 EXAMPLE 4 GOAL2ABCa 22 b 40c 50 70 ft145 ft257 ft290 ft \f!"\n\b#\n\n \n\b\r\f\n I.M. Pei. PeiÕs work is REALLIFEREALLIFE OCUSONPPLICATIONS \t\tFor help with simplifying STUDENTHELP Trigonometric Ratios and Functions/\b\f\b \n\b\r\r\b\n\b \r\f\b\n\b\n\f\r\b\n\b\n\t\r\b8\b\t\f\t\n\b\r\f\t\b\f\n\t\t\r\bBC0\b\f\f6\b\t5\f3\r\t\f4\b0\n\b5\f3\t\t\f\b\r\r\b\r\f -.\b\b\n33\b0\r\n\b4\b\f\n\t\b6\f\n\b0\n\b5\f3\t3\f\n\f\b71\f\t6\b\t5\f3\r \t\n\b\b\n\b\n\t\r\b3\b \n\b0\n\b5\f3\t 3\b0\r\n\b \t\f\n\f\bOLVING OLVING ACB201540 ACB391632 ACB8532 PPLICATIONS Vocabulary Check )*\b.\bto help you master STUDENTHELP STUDENTHELP HOMEWORK HELPExamples 1, 2:Exs. 15Ð37Example 3:Exs. 50, 51Example 4:Exs. 38Ð48Example 5:Exs. 52Ð54 HOOSINGA!&'\n\b\r\f\t\b\fRTISTS4\b3\f\f\n\b0\n\n\n0\bE\b\n\f\n\f\b\n.\b\b\n\r\t\b\t\t\t \n\b,\t\b\b\f4\bF\r \bG\t\n\b\r\b\n\f0\b0\t\n3,\b\tH\nH\t\t\n\n\n\n\bF\n\bG\t\n\b\n\n\n\t\r\bI\r\r\n\b\n3\b\b\n7Source: Trapeze Arts, Inc.URVEYING\b\f\b 3\b\f\t\n\b \f\f\t\f\b\n0 \n\t\f\n\n0\t\n\t\r\b)!#\r\f3\b\f\b\n\b\f\n\t\b3 "\b\b\n \b\f0\b\n\b\r J\n\f\n\b\n\n\b0\t7:\f\t$\r,\t\r\b\n @\t \f\f0\b\r,\b\r\n\r\n\t\t\n\n\n3\b0\b4\b00C3\n\b\r \n\t\r\f\b\n\b\r\t\t* -3\b\n\b\f4\b\b\n\n\b:\f\t$\r,\f\n ! 3\b\n\b\f/\t\n\b\r3\b\n\b ACB412170 ABC847 CAB234 pond BAC56 ft68 ft73 SURVEYOR www.mcdougallittell.com INTERNET REALLIFEREALLIFE OCUSON Visit our Web sitewww.mcdougallittell.com INTERNET STUDENTHELP I 12 ft26 ft5 ft8 ft5 ft Trigonometric Ratios and Functions\f,\t\t\t\n\t\t3\t \t\f\f\f\r\f4\b30\n\n\b\n\f\f\n\b\n\t\f\n\n\b\b\n\b\f\n\b3\t1\f\b\n\b\b\t\f\n\t\b\f\n\t\n\b\b\n\b;\t\f;3\tERTILIZER3\b\f\n\t\r\b\r\n\f\b\f\n\n\b *-\b\b\n !--\b\b\n \t! -\b\b\n\r\t6\b\t\n\f\n00\r \r\r\b\n\rE\b\n\n\b\b\r8\n\n,\b\f\t\b*-0\t\b\n\rE\b\n\b ---\f\b\b\b\n 3\t \f\b\f\b\t\b\b\n\b\n\b\b\r7ULTIPLE40\r\t\b\f\r\b\b\t0\n\n\n\b\f3\b\n3\b \n\b\f\n\b\b\b\t\n\t\n\b\f\b\t\b\b!)#\b\f\n\t\n\n 2--\n\b\f\n\n\b0\n60\n\b\n\b\n0\r\t\b\f7ULTIPLE\r\n\f\b\n\b\n\n\b\r\b3 \b\r\b\n\b\n\n\b\b3 \t\n\b\t\b\r\b\n\b,\n\n\b\r\b3/\t\n\b\f\n\t\b\n\b\r\n\n\b\r\f3\n\b\b3,\n\n\b\r\b3\b\t\n\n\r\r\t\b\b\n\t4\n\f \tL\n\b\n\n\n QUATIONS/2&) - ) -/2- & - ?\b\n\b\f2& - -?\b\n\b\f2- &! - !/2&( - ( -/2?\b\n\b\f2&. - . -?\b\n\b\f2- & - ALCULATING'\b- \n%\b\b\n%\b#%\n\n\r-\t$3 ERTICAL/3\b\n -\b\b\n \r\t\b\f\n\n,\b\r\r\n\t\t\n -\b\b\n0\b\f\b\t\n\n\n\b\t7 MIXEDREVIEW OTbluemirrorred mirror25 6 ft 4.7 ft PIIMM Test EXTRACHALLENGE www.mcdougallittell.com Vernal, UT 108 mi98 mi89 mi64 mi126 mi