Name: Class: Date: _

Quiz Review:Section4.8

Numeric Response

ID: A

I. A helicoptermakesa forcedlandingatsea.The lastradiosignalreceivedatstationC givesthebearingof thehelicopterfromCas N 57.1 E atanaltitudeof 423feet.An observeratC sightsthehelicopterandgivesLDCB as 12.10. How farwill a rescueboatatA haveto travelto reachanysurvivorsatB (seethefigure)?Apply therulesregardingtheuseof significantdigitswhendeterminingyouranswer.

2. Solvethefollowingproblem.Be suretomakeadiagramof thesituationwithall thegiveninformationlabeled.

A shipis anchoredoff a longstraightshorelinethatrunsnorthandsouth.Fromtwoobservationpoints16milesaparton shore,thebearingsof theshipareN 28E and S 50E. Whatis theshortest

distancefromtheshiptotheshore?Apply therulesregardingtheuseof significantdigitswhendeterminingyouranswer.

mt

3. Useacalculatorto find tan 144.50.

Pleaseroundtheanswerto thenearestten-thousandth.

4. Useacalculatorto find sin(- 220) .Distancerescueboattravels= ft

Pleaseroundtheanswerto thenearestten-thousandth.

5. Useacalculatorto find csc 66020'.

Pleaseroundtheanswerto thenearestten-thousandth.

Name:----------

6. Useacalculatorto find () to thenearesttenthof adegree,if 00 < ()

PROBLEM SET 2.4

C~

Figure 13

Figure 14

Solveeachof thefollowingproblems.In eachcase,besuretomakea diagramof thesituationwith all thegiveninformationlabeled.

1. Thetwoequalsidesof anisoscelestriangleareeach42cm.If thebasemeasures30 cm,findtheheightandthemeasureof thetwo equalangles.

2. An equilateraltriangle(onewithall sidesthesamelength)hasanaltitudeof 4.3inches.Find thelengthof thesides.

3. The heightof a right circularcorteis 25.3cm. If thediameterof thebaseis10.4cm, what angledoes the side of the cone makewith the base? (SeeFigure 13.)

4. The diagonalof a rectangleis 348mm,while thelongersideis 278mID.Findtheshortersideof therectangleandtheanglesthediagonalmakeswiththesides.

5. How longshouldanescalatorbe if it is to makeanangleof 33 with thefloorandcarrypeoplea verticaldistanceof 21ft betweenfloors?

6. A roadupa hill makesanangleof 5.1 withthehorizontal.If theroadfromthebottomof thehill to thetopof thehill is 2.5mi long,how highis thehill?

7. A n.5-ft ropefromthetopof acircustentpoleis anchoredtotheground43.2ftfrom thebottomof thepole. What angledoestheropemakewith thepole?(Assumethepoleis perpendicularto theground.)

8. A ladderis leaningagainstthetopof a7.0-ftwall. If thebottomof theladderis4.5 ft fromthewall, whatis theanglebetweentheladderandthewall?

9. If a73.0-ftflagpolecastsashadow51.0ft long,whatis theangleof elevationofthesun(to thenearesttenthof a degree)?

10. If theangleof elevationof thesunis 63.4whena buildingcastsa shadowof37.5ft, whatis theheightof thebuilding?

11. A personstanding150cm from a mirrornoticesthattheangleof depressionfromhis eyesto thebottomof themirroris 12,whiletheangleof elevationtothe top of themirror is 11.Find the verticaldimensionof the mirror. (SeeFigure 14.)

12. A personstandingontopof a 15-fthighsandpilewishestoestimatethewidthofthepile. He visuallylocatestwo rockson thegroundbelowatthebaseof thesandpile.The rocksareon oppositesidesof thesandpile,andhe andthetworocksarein linewithoneanother.If theanglesof depressionfromthetopof thesandpile toeachof therocksare2r and19,how far apartaretherocks?

(

1600:::===========:::::1 Contourinterval=40ft

1in=1600ft

Figure 15

Figure 16

Figure15showsthetopographicmapwe usedin Example4 of thissection.RecallthatStaceyis atpositionS andAmy is atpositionA. In Figure 15,Travis, a thirdhiker,is atpositionT.

13. If thedistancebetweenA andT onthemapin Figure 15is 0.5inch,findeachofthefollowing:a. thehorizontaldistancebetweenAmy andTravisb. thedifferencein elevationbetweenAmy andTravisc. theangleof elevationfromTravis to Amy

14. If thedistancebetweenSand TonthemapinFigure15isiinch,findeachof thefollowing:a. thehorizontaldistancebetweenStaceyandTravisb. thedifferencein elevationbetweenStaceyandTravisc. theangleof elevationfromTravis to Stacey

15. A boatleavestheharborentranceandtravels25 mi in thedirectionN 42E.

The captainthenturnstheboat900 andtravelsanother18mi in thedirectionS 480 E. At thattime,howfar is theboatfromtheharborentrance,andwhatisthebearittgof theboatfromtheharborentrance?(SeeFigure 16.)

Figure17

Figure18

16. A manwanderingin thedesertwalks2.3mi in thedirectionS 31 W. He then

turns90andwalks3.5mi in thecl,irectionN 59W. At thattime,howfar is he !fromhis startingpoint,andwhatis his bearingfromhis startingpoint?

17. Lompoc,California,is 18 mi duesouthof Nipomo.Buellton,California,is dueeastof LompocandS 65E fromNipomo.How far is LompocfromBuellton?

18. A treeon onesideof a riveris duewestof a rockon theothersideof theriver.

Froma stake21 yd northof therock,thebearingof thetreeis S 18.2W. Howfar is it fromtherock to thetree?

19. A boattravelsonacourseof bearingN 37 10'W for 79.5mi.How manymilesnorthandhow manymileswesthastheboattraveled?

20. A boattravelson a courseof bearingS 63 50' E for 100mi. How manymilessouthandhow manymileseasthastheboattraveled?

21. Froma pointonthefloortheangleof elevationtothetopof adooris 47,whiletheangleof elevationto theceilingabovethedooris 59.If theceilingis 10ftabovethefloor,whatis theverticaldimensionof thedoor?(SeeFigure 17.)

22. A manstandingontheroofof abuilding60.0ft highlooksdowntothebuildingnextdoor.He findstheangleof depressionto theroof of thatbuildingfromtheroof of his buildingtobe 34.5,while theangleof depressionfromtheroof ofhis buildingto thebottomof thebuildingnextdoor is 63.2.How tall is thebuildingnextdoor?

23. In Figure18,a personstandingatpointA noticesthattheangleof elevationtothetopof theantennais 4730'.A secondpersonstanding33.0ft fartherfromtheantennathanthepersonatA finds theangleof elevationto thetopof theantennatobe42 10'.How far is thepersonatA fromthebaseof theantenna?

24. Two peopledecideto find theheightof a tree.They positionthemselves25ftapartin linewith,andonthesamesideof, thetree.If theyfindthattheanglesofelevationfromthegroundwheretheyarestandingto thetopof thetreeare65and44,howtall is thetree?

(~

Figure19

25. An ecologistwishesto findtheheightof a redwoodtreethatis ontheothersideCof a creek,as shown in Figure 19. From pointA he finds thatthe angleof .elevationto thetopof thetreeis 10.7.He thenwalks 24.8ft ata right anglefrompointA andfindsthattheanglefromthepathto thetreeatpointB is 86.6.Whatis theheightof thetree?

26. A helicoptermakesa forcedlandingat sea.The last radio signalreceivedatstationC givesthebearingof thehelicopterfromCas N 57.5E atanaltitudeof '426ft.An observeratC sightsthehelicopterandgivesLDCB as12.3.How farwill arescueboatatA havetotraveltoreachanysurvivorsatB? (SeeFigure20.)

27. Two peopledecideto estimatetheheightof a flagpole.Onepersonpositions:himselfduenorthof thepoleandtheotherpersonstandsdueeastof thepole.Ifthetwo peoplearethesamedistancefrom thepole and25 ft fromeachother,Ifind the heightof thepole if the angleof elevationfrom thegroundat"eachperson'spositionto thetopof thepole is 56".(SeeFigure21.)

N

B

Figure20 Figure21

Figure 22

28. To estimatetheheightof a tree,onepersonpositionshimselfduesouthof thetree,while anotherpersonstandsdueeastof thetree.If thetwo peoplearethesamedistancefrom thetreeand 35 ft from eachother,whatis theheightofthetreeif theangleof elevationfromthegroundateachperson'spositionto thetopof thetreeis 48?

29. A satelliteis circling 112mi abovetheearth,asshownin Figure22.Whenthesatelliteis directlyabovepointB,angleA is foundto be76.6.Usethisinforma-tion to find theradiusof theearth.

30. SupposeFigure22 is an exaggerateddiagramof a planeflyingabovetheearth.If theplaneis 4.55mi abovetheearthandtheradiusof theearthis 4,000mi,how far is it fromtheplaneto thehorizon?Whatis themeasureof angleA?

31. A shipis anchoredoff a longstraightshorelinethatrunsnorthandsouth.Fromtwoobservationpoints15miapartonshore,thebearingsof theshipareN 31EandS 53E. Whatis theshortestdistancefromtheshipto theshore?

32. Pat andTim positionthemselves2.5mi apartto watcha missilelaunchfromVandenbergAir Force Base.When themissile is launched,Pat estimatesitsbearingfromhimtobeS 75W, whileTim estimatesthebearingof themissilefromhis positiontobeN 65W. If Tim is duesouthof Pat,howfar is Tim fromthemissilewhenit is launched?

Figure23 showstheSpiral of Rootswe mentionedin thepreviouschapter.Noticethatwe havelabeledUteanglesatthecenterof thespiralwith 81, 82, 83, andsoon.

33. Find thevaluesof 81, 82, and83, accurateto thenearesthundredthof adegree.

c

Figure 23

ProblemSet 2.4

1. 39em,69 3. 78.4 5. 39ft13. a. 800ft b. 200ft c. 14.021. 6.4ft 23. 161ft 25. 78.9ft33. 8\=45.00,~ =35.26,83=30.00

7.. 36.6 9. 55.1 11. 61em15. 31mi, N 78E 17. 39mi 19. 63.4mi N,48.0mi W

27. 26ft 29. 4,000mi 31. 6.2mi

"