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Quiz Review (Section 4.8)

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  Name:Class:Date:   QuizReview:Section 8 NumericResponseID:A I.Ahelicoptermakesaforcedlandingatsea.ThelastradiosignalreceivedatstationCgivesthebearingofthehelicopterfromCasN57.1 ° Eatanaltitudeof423feet.AnobserveratCsightsthehelicopterandgives LDC as12.1 0. Howfarwillarescueboatat   havetotraveltoreachanysurvivorsat   seethefigure)?Applytherulesregardingtheuseofsignificantdigitswhendeterminingyouranswer.2.Solvethefollowingproblem.Besuretomakeadiagramofthesituationwithallthegiveninformationlabeled.Ashipisanchoredoffalongstraightshorelinethatrunsnorthandsouth.Fromtwoobservationpoints16milesapartonshore,thebearingsoftheshipareN28°EandS50°E.Whatistheshortestdistancefromtheshiptotheshore?Applytherulesregardingtheuseofsignificantdigitswhendeterminingyouranswer. mt 3.Useacalculatortofindtan144.5 0. Pleaseroundtheanswertothenearestten-thousandth.4.Useacalculatortofindsin -220)°.Distancerescueboattravels  t Pleaseroundtheanswertothenearestten-thousandth.5.Useacalculatortofindcsc660°20 .Pleaseroundtheanswertothenearestten-thousandth.  Name:   6.Useacalculatortofind tothenearesttenthofadegree,if0 0 <()< 360°andsin =- 0.3060with inQIII (}= o 7.Useacalculatortofind tothenearesttenthofadegree,if0 0 < <360°andsec =- 3.4150with inQlI (}= o ShortAnswerUseacalculatortoevaluatethecotangent,secant,andcosecantoftherealnumber.Roundtofourdecimalplaces. 9 1= 1 1 Useacalculatortoevaluatethesine,cosine,andtangentoftherealnumber.Roundtofourdecimalplaces. 1r 10 1=5 Useacalculatortoapproximatetheexpression.11.arcsin0.252ID:A8.Useacalculatortofind tothenearesttenthofadegree,if0 0 <()< 360 ° andcot =- 0.7395with inQlI (}= o Useacalculatortoapproximatetheexpression.12.arccos -0.62 u z Review:Section4.8AnswerSection NUMERICRESPONSE I.l, LN 2.5.93.-0.71334.0.64285.-1.15866.197.87.107.08.126.5SHORTANSWER9.cot 1 =0.5090;sec 1 =2.2046;csc 1 =1.122110.sin 1 =0.5878;cos 1 =0.8090;tan 1 =0.726511.0.2512.2.24  PROBLEMSET 4 C~ Figure13Figure14Solveeachofthefollowingproblems.Ineachcase,besuretomakeadiagramofthesituationwithallthegiveninformationlabeled.1.Thetwoequalsidesofanisoscelestriangleareeach42cm.Ifthebasemeasures30cm,findtheheightandthemeasureofthetwoequalangles.2.Anequilateraltriangle onewithallsidesthesamelength hasanaltitudeof4.3inches.Findthelengthofthesides.3.Theheightofarightcircularcorteis25.3cm.Ifthediameterofthebaseis10.4cm,whatangledoesthesideoftheconemakewiththebase? SeeFigure13. 4.Thediagonalofarectangleis348mm,whilethelongersideis278mID.Findtheshortersideoftherectangleandtheanglesthediagonalmakeswiththesides.5.Howlongshouldanescalatorbeifitistomakeanangleof33°withthefloorandcarrypeopleaverticaldistanceof21ftbetweenfloors?6.Aroadupahillmakesanangleof5.1°withthehorizontal.Iftheroadfromthebottomofthehilltothetopofthehillis2.5milong,howhighisthehill?7.An.5-ftropefromthetopofacircustentpoleisanchoredtotheground43.2ftfromthebottomofthepole.Whatangledoestheropemakewiththepole? Assumethepoleisperpendiculartotheground. 8.Aladderisleaningagainstthetopofa7.0-ftwall.Ifthebottomoftheladderis4.5ftfromthewall,whatistheanglebetweentheladderandthewall?9.Ifa73.0-ftflagpolecastsashadow51.0ftlong,whatistheangleofelevationofthesun tothenearesttenthofadegree ?10.Iftheangleofelevationofthesunis63.4°whenabuildingcastsashadowof37.5ft,whatistheheightofthebuilding?11.Apersonstanding150cmfromamirrornoticesthattheangleofdepressionfromhiseyestothebottomofthemirroris12°,whiletheangleofelevationtothetopofthemirroris11°.Findtheverticaldimensionofthemirror. SeeFigure14. 12.Apersonstandingontopofa15-fthighsandpilewishestoestimatethewidthofthepile.Hevisuallylocatestworocksonthegroundbelowatthebaseofthesandpile.Therocksareonoppositesidesofthesandpile,andheandthetworocksareinlinewithoneanother.Iftheanglesofdepressionfromthetopofthesandpiletoeachoftherocksare2rand19°,howfarapartaretherocks?   1600  =========== Contourinterval = 40 ft 1in=1600 ft Figure15Figure16Figure15showsthetopographicmapweusedinExample4ofthissection.RecallthatStaceyisatpositionSandAmyisatposition   InFigure15,Travis,athirdhiker,isatposition T 13.Ifthedistancebetween   and T onthemapinFigure15is0.5inch,findeachofthefollowing:a.thehorizontaldistancebetweenAmyandTravisb.thedifferenceinelevationbetweenAmyandTravisc.theangleofelevationfromTravistoAmy14.IfthedistancebetweenSand  o themapinFigure15is i inch,findeachofthefollowing:a.thehorizontaldistancebetweenStaceyandTravisb.thedifferenceinelevationbetweenStaceyandTravisc.theangleofelevationfromTravistoStacey15.Aboatleavestheharborentranceandtravels25miinthedirectionN42°E.Thecaptainthenturnstheboat 900 andtravelsanother18miinthedirectionS 480 E.Atthattime,howfaristheboatfromtheharborentrance,andwhatisthebearittgoftheboatfromtheharborentrance? SeeFigure16.  Figure17Figure18 16.Amanwanderinginthedesertwalks2.3miinthedirectionS31°W.Hethenturns90°andwalks3.5miinthecl,irectionN59°W.Atthattime,howfarishe   fromhisstartingpoint,andwhatishisbearingfromhisstartingpoint?17.Lompoc,California,is  8 miduesouthofNipomo.Buellton,California,isdueeastofLompocandS65°EfromNipomo.HowfarisLompocfromBuellton?18.Atreeononesideofariverisduewestofarockontheothersideoftheriver.Fromastake21ydnorthoftherock,thebearingofthetreeisS18.2°W.Howfarisitfromtherocktothetree?19.AboattravelsonacourseofbearingN37° 10 Wfor79.5mi.Howmanymilesnorthandhowmanymileswesthastheboattraveled?20.AboattravelsonacourseofbearingS63°50 Efor100mi.Howmanymilessouthandhowmanymileseasthastheboattraveled?21.Fromapointonthefloortheangleofelevationtothetopofadooris47°,whiletheangleofelevationtotheceilingabovethedooris59°.Iftheceilingis10ftabovethefloor,whatistheverticaldimensionofthedoor?(SeeFigure17.)22.Amanstandingontheroofofabuilding60.0fthighlooksdowntothebuildingnextdoor.Hefindstheangleofdepressiontotheroofofthatbuildingfromtheroofofhisbuildingtobe34.5°,whiletheangleofdepressionfromtheroofofhisbuildingtothebottomofthebuildingnextdooris63.2°.Howtallisthebuildingnextdoor?23.InFigure18,apersonstandingatpoint   noticesthattheangleofelevationtothetopoftheantennais47°30 .Asecondpersonstanding33.0ftfartherfromtheantennathanthepersonat   findstheangleofelevationtothetopoftheantennatobe42°10 .HowfaristhepersonatAfromthebaseoftheantenna?24.Twopeopledecidetofindtheheightofatree.Theypositionthemselves25ftapartinlinewith,andonthesamesideof,thetree.Iftheyfindthattheanglesofelevationfromthegroundwheretheyarestandingtothetopofthetreeare65 ° and44°,howtallisthetree? (~ Figure  9 25.Anecologistwishestofindtheheightofaredwoodtreethatisontheotherside C ofacreek,asshowninFigure19.Frompoint   hefindsthattheangleof.elevationtothetopofthetreeis10.7°.Hethenwalks24.8ftatarightanglefrompoint   andfindsthattheanglefromthepathtothetreeatpoint   is86.6°.Whatistheheightofthetree?26.Ahelicoptermakesaforcedlandingatsea.ThelastradiosignalreceivedatstationCgivesthebearingofthehelicopterfromCasN57.5 ° Eatanaltitudeof 426ft.AnobserveratCsightsthehelicopterandgives LDC as12.3°.HowfarwillarescueboatatAhavetotraveltoreachanysurvivorsatB?(SeeFigure20.)27.Twopeopledecidetoestimatetheheightofaflagpole.Onepersonpositions:himselfduenorthofthepoleandtheotherpersonstandsdueeastofthepole.Ifthetwopeoplearethesamedistancefromthepoleand25ftfromeachother, I findtheheightofthepoleiftheangleofelevationfromthegroundat eachperson spositiontothetopofthepoleis 56 . (SeeFigure21.) N B Figure20 ã Figure  
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