Post on 29-Jan-2023
.--,,!d .:iirlg trig tunctions ol'an acute
ilt tllat':" -, ,Ectti ansr'cr t in table [urnr ) using
Gite a '"-- '
Section 6.6 The Trigonometry of Right Triangles
Use a calculator to fincl the value of each expression'
rounded to four decimal Places'
24. cos'l2o :"'';'
26. cot 57.3' r, i'
28. csc 39' , .:'t,:,
25. tan 40" rr . ,,r
27. sec 40.9" :.1
29. sin 65' :",'.'''
23 through 30 to answer.
31. sin A : 0.4540 -r',i
33. tan 0 : 0.8391 ':.!:
35. sccB - l.12-10
37. sin 4 -- $.906.3
39. tan a : 0.9896 :': ':
41. sin r-v - 0.32153
74..120 lt '------ -- ll
-'{
iriangies slhown and lvrite answers in tatrle
;.i ri?*t to the nearest 100th of a unit' Yerify
sum to 180'and that the three sides satisfy
y) 6he PYthagorean theorem'
18.
))
0es,
Use a calculator to find the acute angle whose
corresponding ratio is given' Round to the nearest l0th
of a degree. For Exercises 31 through 33' use Exercises
16.32. cosB:0.3090
34. cotA :0.6420
36. cscli : 1.5890
38. lanB:9.6'768
40. cosa:0.7408
42. tana : 3.1336
43.
Select an appropriate function to find the angle
indicated (round to l0ths of a degrec)'
44.
18.7 cm
221 yd
47.
14 in
18 rr
i9.5 cm
45.8 m
CHAPTER 6 An lntroduction to Trigonometric Functions
f)rary a right triangle ABC as
shown, using the informationgiven. Then select :rn appropriateratio to find the side indicated.Round to the nearest t00th.
19. LA : 25" :, :r ,
c : 52 rnntfind side a
Sl" /A:32. :ilria : 1.9 ilifind side ll
53. LA: 62.3'b : E2.5 furlongsfind side c
55. sin 25', cos 65'
56. sin 57". cos 33"
57. tan 5", cot 85o
58. sec 40o, csc 50o
tlased on )our ohseryations in Exerr:ises i.i r^ -
the blank so that the functions given ".- -ijl,]t
Exereises 49 to 54B
Use a calculator to evaluate each pair offunctions andcomment on what you notice.
59. sin 47 . cos
- 60. e ,,s ..-. \in
I
61. cot 69o" tan -: ,' 62. csc tl", sec,il
Complete the following tatrles withouf re{'erringtext or using a calculator. o
6J.
Evaluate the following expressions withoaat a ca
using the cofunction relationship and theforms: sec 75" = \/6 + rt; tan 75" = 2 +
64.
s0.
52.
54.
LB : 55"b: 31 ftlind side c
L_8 - 29.6'r: : 9.-5 ydhnd side a
LB : 12.5"a : 32.8 kmfind side l:
b w*ffiHEru* &qf$YM F*ffitrllLiE-,&S
69. The sine of an angle between two sides of a
triangle: sintl =4ab
If the area lt and two sides a and b of a riangle areknown, the sine of the angle between the two sidesis given by the formula shown. Find the angle 0 forthe triangle shown given "4
: 38.9, and use it tosolve the triangle. {Hint: Apply the same conceptto angle 0 or ry.)
lcos070. Illumination of a surface: E =
The lllumination E of a surface by a light source isa measure of the luminous flux per unit area thatreaches the surface. The vah-re of E fin lumens (1m)
!,,irirt;i.:riri :;r-,:r-"::.i r::iir i-r: lrrLr11; ilt lltt lr.;lrlrrh-,i ...!!r:.i.,1:i 1a-,.-.--.- ..
65. {6 csc 15" t'j . :\.:'i 66. csc2 15o
67. cat2 15" i t ::...'',, 68. ru€cot
per square foot.l isgiven by theformula shown,where d is thedistance from thelight source (infeet), I is theintensity of thelight [in candelas(cd)1, and 6 is theargle the lightsource makes withthe vertical. Forreading a book, an
illumination E ofat least 18 lm/ft? isrecommended.
I (o :
A\17,." '\g,.. \,4N
24
d2Assuming the open book is lying on a hotl€
surface, how far away should a light soulcqplacerl if it has an intensity of 90 cd (aboLtt
and the light flux makes an angle of 65" wll
0 = 30o sin 0 cos 0 t:rn s
cos(90" -. 0) ' tan(90' - 0) csc 0 sec S ::
0=45" ; sin4 cos9 tan$. si
cos(90' - B) : tan(90o - 0) : csc 0 sec (}
book's surface (.i.e.,0 : 25")? ;,i,r:r:r.: l ll
,;^ ^r olevation: In 2001, the tallest building in
:::^:;;. the Petronas Tower I in KualaWult" '' - r:-- f < o frl:i."#;rsia. For a person standing 25'e ft
Iitrlr; ;;;" of tt.," tot".i, the ang1e.of."1":':i:i t:
lop "iirr. tower is 89o' How tall is the Petronas
r,,oole o{ depression: A person standing oear the
::.;; to. Eiffel Tower notices a car wreck some^
Ii*.. f** the tower' If the angle of depressron
il;h; person's eyes to the wreck': :2:' how far
'a1], it"tt ,".rdent from the base of the tower?
*eYt*r4S
" ofeievation: For a person *11dly'99 T:Ji ""ri"i"i the base ol the E'iffel Tower' the
';;;;;;"' to the toP of the tower is 7 I '6" '
,iit i, tt'," EiffelTower?
Exercise 7 i '
*".tcise 72.
es ofl rotation::l.,,fioma point 110 fti.due south of theeastern end of a
|i::::1,,97a**ed eas t/w e s t
??. Height of a climber: A local Outdoors Club has' '-
irt,-r',iL"d to the south rim of a large canyon' when
iir"y tp* a climber attempting to scale the ta11er
noirfl"tn face. Knowing the distance between the
sheer walls of the nortiern and southern faces of
the canyon is approximately 175 yd' they attempt
i"."Lp*" the distance remaining for the climbers
to reach the top of the northern rim' Using a
homemade transit, they sight an angle of
a"pt"t.ion of 55' to the bottom of the north face'
uni ungt", of elevation of 24" and 30" to the
climbers ancl top of the northern rim respeclively'
Section 6.6 The Trigonometry of Right Triangles
(a) How high is
the southernrim of the
canyon?(b) How high is
tire northernrim'? (c) Howmuch fartheruntil the climber
lhe ground. From a
clistance of 500 ft the angle
of elevation lo the Pinnacleof the tower is 74.6'. The
angle of elevation to the
restatlrart from the same
vantage Point is 66'5"'How tal1is the CNNTou,er? How far below the
pinnacle of the tower is the
reslallrant located?
607
$;X" of depression: A person, standlng on the
, ;;";i it,* P"tronut Tower L""*t::::"^:::'::iil ,rO pi"points her residence' If the angle ol
s/Wp, i u;o" fro m the p er^s on' s tI
: t'o,
l "l 1 : :t^,t|T.\l,in* f:u away (in feet and in miles) is the
*1i,f"".* from the base of the tower? See
leachesthetop?. .i, ,- ,,.,.,.,,r,:I,rl'r ;.1::1lr''rli. ':1tl-11
"i.1 !'l :1ir:rirl! ' : ' ": t 't '' 'l r,,'
73. bililili"g'*lafii.t From her elevated observatton
post 300 fi away, a naturalist spots a troop ol
ilrUnont high up in a tree' Using the small transit
attached tollerielescope. she finds the angle of
a.fi"*tion to the bottom of thts tree is 14"' while the
orgt" of elevation to the top of the lree is 25"' The
,n!f" of elevation to the troop of baboons is 2l "'
Usl this information to find (a) the height of the
observation post, (b) the height of the baboons' lree'
1ro i.t iry 1;lchlg:,rk ?pogns a!,!y€,891d,,
Zq. lngl" of elevation:'The tallest free-standing lower
in tie world is the CNN Tor'ver in Toronto' Canada'
Thetowerirrclrrdesarotatingrestatlrantlriglrabove
ri1;,bridge spanning the
t,l.'::.lllinois river, a surveyorrnotcs llre western end
rlies on a bearing of,N 38'35'15'w. To the
jl:,.i1earest inch. how lolg
Yill f. bridge be?
Angles of rotation: Alarge sign spans aneastlwet:r highway.From a point 35 m duewest of the southern base of the sign, a surveyol&nds rhe northern base iies on a bearing ofN 6?" I '1'42" E.To the nearest centimeter' horvwide is the stgn? t-, ; , rr,
,|I
N EO.
i,:i r1,... li't:....' :.1 1!'l'' '' I
iret" or "i.ouiio-h-,
ln Jonuuty 2009' Bul.Dubai
.;;"?fi.i;it captnrecl tlre record as the world's rallesi
l,.,if Ai"g, o..oiaing io tl-re Councii on Tali Buildings
ancl Ur-ian H abittrt ('S o tt rc e : www'ctbuh'or g)'
ftf"^tl.,."d at a poiilt 159 rn trom its base ' the lingle
of eierration to ih" top of the spire is 79' Ftotr a
Xi 35m
/rurKffi- lffiIHffi'Mr&q
t, 1' :1 ':':"' '
768 CHAPTER B Applications of Trigonometry
35. Alternative form for the law of cosines:
h2+c2-s)COSA :
2hcBy solving the law ofcosines for the cosine ofihe angle, the formlrla Acan be written as shown.
36. The perimeter of a trapezoid:P=a+b+/z(csca*cscB)
39. Runway length:Surveyors aremeasuring a large,marshy area outside ofthe city as part of aleasibility study for theconstruction of a newairport. Using a
theodolite and themarkers shown gives
The perimeter of atrapezoid can beforind using thelbrmula shown,where a and brepresent the
with base angies a : 42" ancl p : 76. ,:
Derive-this formuia (solve for cos g), beginningfrom ar : b2 + t;t - Zb, cos A. then us*e this formto begin the solution of the triangle given. :,. .. .,1;.:.:,
37. Distance between cities: The satellite Mercury IImeasLtres its distance from portland and fiomGreen Bay using radio waves as shown. Using anon-board sighting device, the satellite determinesthat LM is 99". How many miles is it fromPortland to Gleen Bay? ;)ir;:rr :r',' ..,
Mercury II
Poltland n7 Green Bay
Distance between cities: Voyager VII measures itsdistance from Los Angeles and from San Franciscousing radio waves as shown. Using an onboardsighting device, the satellite deternines LV is 95".How many kilometers separate Los Angeles andSan Francisco?
the information indicated. ll'the mairr rlrnwaybe at least 1i,000 ft long, and environraental',
4$.
38.
on a proposed tunnel through Harvest &4ountaiorder to find the tunnel's length, the mea
(b) Due to previous tunneiing experience, theestimates a cost of $5000 per foot for boring-
management insists ol a25Vo proflt, what wil,l
37 nr
Voyager VII
610 yd
San Franciscr-r Los Angeles
Iengrhs o[ rhe pal.allel sides. ii is rhr. i:..ilhr ^ctrapezoirl, and a anrJ P l:,5,?l:",1.,:-,';:: ;ij:)rlre pcrimetel oi'Trapeztrid Par.k , ,n ,,,. n.r*l',toot) iI a - 5000 lr. h - 7-500 t'r. .nc l, =-r,i],..
concerns are satisfied, can the airport be consiiucat this site (recall thar I rni = 5280 tri.''
.: l
Ttrnnel length: An engineering flrm decides to bi
shown are {aken. (a) How long will the tunoelii$
through this type ofrock and construcring the i
tunnel according to required speciflcations. lf .,
their minimum bid to the nearest huncJred? ,,.
Section 8.2 The Law of Cosines; the Area of a Triangle 769
i'iri": -'ness executive is going to fly6ip ptanningt l: out';,
,:r^r^^ +^ Cnnaoe cove.:ffi;;ffi from P,ovidenc:]:.:::""t:::'"
$, J*i.orx"i'* t':T:::"*::: "T31 l#il;l; ffi ;;i, *^',,. I:' Tr"::1': :l:::"':l-"*:
::jl ;ffi;;ii;"' what is the measure of angre
l',,,' Iri*" heading-sh.ould she set for this trip?li#;-o;i'""Ji1e.;1.9u1d
she set ror this trip?
45. Geoboard geometry: A rubber land ls
11aced on a
-'' ;;";;oiu-uo*o with ali pegs 1 cm apart) as
shown. Approxtmate the perimeter of the triangle
;;;"; uvir'," rubler baid andthe angle formed at
each vertex. (I{lnr Use a standard triangle to find
/*A andlength AB'),' :,': t'"'tt''l "" l:1r''' jl "'ll' l' i'" l1'1!"
Exereise 45
"d;;:;ffig should theY set for this triP?
60Ge€soo0OGGOG&
OGGOcls&&6
Exercise 46
ssa*soaoo0coso6S&46
oocs0oo--\L
MMannerlY Main
c:423mi
College Cove
NorthI
WesrAEastYSouth
: ti4 mI
Providence
46. Geoboard geometry: A rubber band is piaced on a
geoboard u, 't'otn'
ipproximate the perimeter of
the triangle formed UV if'" ruU!31band and the
angt" folm"a at each vertex' (F/irr: Use a
n'?rlrr,".13"t I'il1"l.:}'l l$ irsti 1'l) of Scouts is Planning aTriP Planning: A trooP
lrif.i iro* Montgomery to Pattonvill"' theY -'
,i-f.t U* the distances shown u.si19,a *11:.Yng
*;Jrtr;". for reference since it is due east of
il,,l,fr;;;;;;rrv' what is the measure,gt iill" ''
10 mi ln Exercises 47 and 48, three rods are atlached via pivot
il;;;;il; rods can tre manipulated to fo'm a triangle'
'f#1fr" three angles of the triangle fbrmed'
3r,,.Aerlal distance: Two planes leave LosAngeles
,, -,International Airport ui th" turnt time' One o'l:it^il t;;;A rr"rii*e 270') with a cruising speed of
4t0;;,';;ing tn for.vn. J'po:: witha sroup that
seeks i,"anluiliiy at the ro919r \4.ount I lll- ] :"
olhe, rareis at heading 225' with a cn"rising.-speed
of 421 rrrph. going to Brisbanc- AustraliiL' with a
lgro.rp ,""kin! udrent.,re in the Great Ou.*utl:..^--
Nautieal distance: Two ships leave Htl-ntrlultr
Harbor at the same time. One tlavels 15 knots
in.r,i.,J *ii., p",. t-,out, at lreading ll0''-1Tl itgoinl i,r r5e Mapoucsu< lslanclt (Croshy' Stillt' anJ
't"I.',; i'ii. ottrer-tlavels i2 knots at heading 200"'ano;s going t; the Samoan lsiands (.Samttct',1^e galuq tu). *owiar apart are the two ships after 10 hr?
47.
:tl:.l" [ppl rr:;;d; airtrr." between the planes after
5 hr o{ 11lght. rr,r:r..r :,rl
49. Peniagon Perimeter: Frnd the
apploximate Perinreter oi zi
regLta. Pentctgot'L lht.rl is
.ii.u-*..it'"d bY a circle rvith
ruJitts i' - l0 cm'
50. Hexagon Perimeter: Find the
perimeter of a regular herogott
ihat is circumsciibed bv a
circle with radir:s r : i5 cm'
Exercise 49
,/\/\/ ttt "tt' \II\l\/\./'-\
Hd
\"1t1.I
i
i
1
i
I
7i754
sin 32o sin i8.5"t. 15rl
11.
9.sin 63' sin C
21.9 18.6
sin C sin 19o
ri6.) +3.1
13. side a: J5 cmLA - 38"
/ D -
A1aLD - +It-. ,.,, l1,l' . tr ..., lilll.,: i;:t- r.. ,. I :,,"1
15. side b : 1016 in.LA: 30'/B:60" ,ti.; =
16.
lia::i1{xw*sH i gl[r-:d]{ilt *L:: *h
CHAPTER B Applications of Trigonometry
e" *,{iiq{: iltri"$ *ff * xii)'*;:i !*{i !-;4,*l;
Fill in each blank with the appropriate rvord or phrase'
1. For the law of sines, if two sides and an angle
opposite one sicle are given, this is referred to tts
the i :,':ir::r'ir.r', CaSe, SinCe the SOlutiOn iS in dOubt
until iurther work.
3. For positive k < l, ihe equation sin 0 = /c has two
soir-ttions, one in Qr-iadrant and the other
in Quadrant
5. In your own words, explain why the AAS case
results in a unique solution while the SSA case
does not. Give supporting diagrams.I :!!ir. ::.,.. i.tit I t::..,
e *HV$EL*plrds Y*Liffi sKitLs
Solve each of the following equations for the unknownpart (if possible). Round sides to the nearest hundredth
and degrees to the nearest tenth.
sin 52" sin 30o8._D IL
li . l:'l !.::
sin B sin 105"10.
- : ---'--3.14 6.28
;'r' : 'i': r':
sin 38o sin B
125 190; ; -.' i,' ;.-:. '
ffi Solve each triangle using the law ofsines. Ifthe law offfi sines cannot be used, state why. Draw and label a
triangle or Iabel the triangle given before you begin. Use
a calculator to verify your results.
14. side b : 385 mLB: 47"LA: la&"
ir.) .,:....(_ ,,.'-,-:,, -, -,-. -.iilil.,'lt. r. ,-, -lll
Carefullv reread the section if needed.
can exceed
4. After a triangle is solved, you sl-roulcl nlr,y
to onsure that the :'r:tr'' ; side is oppoii_- arrglc.
6. Explain why no triangle is possible in eai(a. A:34',8 :J3",C: 52, ..
a: !4"b:22"c: 18', .,.,,,
b. A : 42",8 : 57o,C: 81",,.,.,,a=1".b-9",c )2"
---: 19 in.
89 yd
2. Two inviolatc propettics o{'I trir,lrle 1i111 ,,,.
used to help solve the ambiguou'' ':*t" ul.iflangles must slllr] to ' and (b) no ii"l
19. LALB
side c
21. LBside zr
LC
/i -Ln-
side c :/D-LD*
r;{i,1." r:
20.4i ...i:l
I2.9 mi?:45. 2$._ /<o: r5i2mtij :::r- l; ,"" l:i r:ti -a {:: 103.4o: 42.7 km: 19.6' :t :\ '. :',i '. i:
)",
755Section 8.1 0blique Triangles and the Law of Sines
34.
35.
2'l .5 cm
each question and justify your response usrng a ./38" ,but do not solve'
b
DD
llt.9kty,/,"'
,,:^"
r:t,,on AABC wifh LA: 30o and side c : 20 cm'
iri*r,-, r."grh ror side i ytllt,:*:L1Ll.I^u ,,H;;;i ab) row manv triangles can be formed if
;;;.-; : 8 crn? (c) If side a : l2:m, ho;1manv
:,iio*i"^nv triangles can be formed?
;&i;;;'U;b *i* LA : 60" and side c 1 f V: m'
:{;i *fr^r length for side a will produce a right
l6l3ng1e'? (b) How many triangles can be formed if
36.
37.:...i t.1
:.1
I llilriia" "
: B m? (c) if side a : l0 m' how manY
l.gr", can be iormed? (d) If side a : 15 m' how
many triangtes-.can be formed?1,-jl r ::. lr e, j {1. :
g the law of sines and a scaled drawing' If twtt
exist, solve both comPletelY'
l*iide b : 385 m 28.6'1"
490 m
side a :LB:
side & :t:r.l t.rit:ttrirll:
side c :1-A -
s10e al -'.r _lr: . i.
side b :LD-
side a :
36.5 ydo/12.9 yd
10r,6 in.60"15 in.
Z+.9 t<n-,
32.8 km
lhe taw of, sines to determine if no triangle, one
38. B 6o./-{''-/grr'.s/ _q"'/_4,/+/'
q,/u-,./
,, l)
For Exercises 39 to 44, assume the law of sines is being
applied to solve a triangle' Solve for the unknown
,iei" fif possible), therrdetermine if a second angle
i0'-l ; < 180') exists that also satislies the proportion'
25,8 mi30"17.9 wi
,. il':'i
58 mi59"67 nii
30.
7,)
be formed from the€' or two triangles can I
ms given (diagiams may rtot be to scale), then sin 48"
21
sin 57' _35.6
sinA sin 15'ot' ,*o
: 52
sin 60'4$' 32
sin B
If trvo solution.s exist, solve both completely' Note$!!orvhea* marks the side of undetermined length'
-itt ft ,/
39.
41.sin C t.,laL.
40.2
sin B sin 65'<') Lq
ry:Z _ sin B
121 321
382 cm
1_44.
rve the triangle in Exercise 2 using only the law
;;i;.'' then bv using the Y:f ":t-'.1"', ., ^^$;;y the law of sines' Which method was
;li-ie efficient?f :1. f '. t' " I 29'!"' n * It) 'l ttt. lit*' ttl srtics
6. Begin with a2 : bz + c' * 2b' cosA and write
cos A in terms of a, b, and c (solve for cos A)' Why
must b2 + c2 * az < zbc hold in order for a
solution to exist? r
. t,tt- l',,.'- =l''1 ' ''.ir, ,,:- r,1 >2b,.,.
., . *-. 11":":::":l'l' r!':"::.n"'
1.
fr;' .''l:'n '".''li'f."' ' .
ffi Solve using the law of cosines (if possible)' Latrel each
EH triarrgle appropriately before you tregin' Use a
calculator to verify your results'
24. s 25. s
Section 8.2 The Law of Cosines; the Area of a Triangle
6.7 km
C
767
iiu *t .tt *t the law of cosines can-be used to
solution process for each triangle'
30 km
15 mi
12. ves
CC
i$':f ;i,? !e ,, ,.n,
27. side c : 10\,5 in.sideb: 6tzin.sidea: 15rEin.
28. side a:282ftsideb: 129ftside c : 300 ft i1
29. side a: 32.8kmsideb:24.9kmside c : 1Z.4km
30. s
'- : l:lr, /. lil a' -',..
= {i? 5'. 3 * 1j.4". {' - 85,1 "
,1 ,= 119.3",8 - 41.5". ., - l!.1''
8.
10. iloAC
26.
15 yd
: i:11:iiil:lrr.,lr
tli,ili
j. j.tl
.$l:,i.
ach triangle, verify all three forms of the law of
1. of the following equations fur the unknown
4?,',= 52 + 62 - 2(5)(6)cosB i*4i.'r"
2.92 : 15.22 + 9.82 - 2(15.2)(9.8)cos c c'= 57'i"
if,,,: 92 + 12 - 2(9)(?)cos 52' a - :t.24
$ = 122 + 152 - 2(12)(15)cosA A:4i6'
!,K2' = lB22 + 982 - 2082X9s)cos I r '= E6 e
!:reach triangle using the law of cosines. Use a
to verify your results.
:siaea:75cm 22. side b: 385 mLC:67"
sidea:490m;l.'.' {:6.8'. d = 46'1", r = il9{}'8 rlr
l"C = 38o
iic..:zt-ri*i.LB = 36ldea: l2.9mi A.:13.8,'.f .= 1:6.1'.r''- l$rir
2.9 x tOts rrri D
33.sidea:12{1Ydsideb: l2.9ydside c : 9.2yd A - ile'7" ii -'21 ?'. tj: i6.6''
34. side a : 36.5 AUsideb: l2.9AUside c : 22 AU nor Posriblc
Arklitionll anslveL-r cilil bc 1*Llrril in lhe lllsti.ue$l Alls\Ycr AlrlrlLL \
,"4.
.;)
1iU
o/xlal -at L,'C
A
6.8 AU
49 cm
1114;1 *i
208 cm
For Exercises 8-1L, make a sketch of each compass reading' 10.
11.
8. N70"E 9. N10'W 10. s15"E
12. Match each compass direction with a course'
Direction Course
northeast 135"
southeast 225"
northwest 315'southwest 045'
13. A famous Alfred Hitchcock movie is North
by Northwest. This direction is midway be-
tween north and northwest. What course cor-
responds to this direction?
14. From one corner of a triangular plot of land, a
surveyor determines the directions to the
other two comers to be N32"E and 576"8'
What is the measure of the angle formed by
the edges of the plot of land at the corner
where the surveYor is?
In Exercises 1-4, draw a diagram like those in class Exercises 3-6 to show the
path of a ship proceeding on each given course'
ffi t. o7o' 2. 150" 3' 340' 4' 225'
5. i::;:r:];iliL:;-: Ship A sights ship B on a compass bearing of 080'' Make a sketch
and give the compass bearing of ship A from ship B'
6. li,,:'itil;;;lll ShiP X sights shiP Y
on a bearing of 308". What is the
bearing of X from Y?
7. !y'i',;1;t.1;111 An airplane flies on a
course of i 10" at a sPeed of1200 km/h. How far east of its
starting point is it after 2 tr?
8. A hunter walks east for t h and
then north for lj h. What course
should the hunter take to return [o
his starting point? What assumP-
tions do You make to answer the
question? l#h:$efi?jrffig.PointBisl0kmnorthofpointA,andpointCisl0kmfromBonabearingof
060' from B. Find the bearing and distance ol C from A'
11. S40'W ',.
ffirt
362 Chapter Nine
:i
10.
11.
Point S is 4 km west of Point R' and
point I is 4 km southwest of S' Find
ih" b"aring and distance of R from I'i.r',',: i., 1, ,', Traveling at a speed of
10 knots, a shiP Proceeds south from
its port for I-] h and then changes
.ouir" to I30" for I h' At this time'
how far from Port is the shiP?
lr;r,1 11r;,,',: A sailboat ieaves its dock
and proceeds east for 2 mi' lt then
changes course to 205" until it is due
south of its dock. How far south is
this?
t,
13.
travel to reach shiP A?
Two shiPs, A and B,
leave port at the same time' ShiP A
pro"."d, at 12 knots on a course of
b40', *hil" ship B proceeds at 9 knots
on a course of 115'. After 2 h, shiP A
loses power and radios for help" How
far anO on what course must shiP B
14.
ln Exercises 15-18, sketch each plot of land described and find its area'
,,.1;,,:, 1 ,:,11 11 A ship leaves port and sails northwest for t h and then northeast
for 2 h. If it does no, tf'ung" speed' find what course the ship should take to
return directly to port' efJo fina how long this return will take'
.: :; : :. From an iron post, proceed 500 m northeast to the brook' then
300 m east along the b;k to irtf ota miil' then 200 m S15"E to a post on the
edge of Wiggin', noua, una nnuUy along Wiggin's Road back to the iron post'
l::r;;r",, , From a cement marker' proceed 26A m southwest to the river' then
240 msouth along the river to the bridge' then 280 m N40"8 to a sign on the
edge of Sycamore f-u'", ut'O finally along Sycamore Lane back to the cement
marker.
i:.
i:l
!r
ffi 15.
16.
17. r::irr.,r-.,:,,., From the southeast comer of the ""T"1",?"-o:^::*::,::it;nl".""utr*#;J;t,;;';G'l^l':"ft ."3t:'*H"*'i"i:*il:?;;.;1;ilHi""";#;i#;,";';;:r;"E:';l'o*i::,ol::'*::;:'Ji:,:J,[::iffi""il}! -# "*i i,-i,i"rr""r. Bumham Road, and finallv N30'E along
gumtram Road back to the starting pomt'
lg. l,:u;.lrr.ri::! From rhe intersection of Simpson's.Road *yJlt^:T-kT";0il";;;i' *i;;ri' "'
fi ;;;f ii*p' o,'' Ro ad, then : t'.T
-t:'.,'-1?, :J*3;ffi'#i.J,1iii""r'j:r'ffii;ffi;; ;," is reached, and finauy N68'E
along Mulberry Lane back to the starting pomt'
Triangle TrigonometT 363