Rd sharma class 10 solutions some applications of trigonometry

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RD Sharma Class 10 Solutions Applications of Trigonometry
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toi,:r' -(-.o.' pP.'t O = po.r-16; - 36".,.
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Jn e fg t-,t-
E. J5o bc,fld .%.1
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od cp Lz, .t92
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5i
r{ g ,lq-e.
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A
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0f i5:
? &o-=
+L=
rt
!:l = -+') 'n
loq-26t alova
bet tteen tor.,sc
"
: .J. S.x l.+B L
= 12'11
-t.
6rot-o,J - .A r-o,
= lqt+.S _ '2>.S"o.
arJ t..ftdf-q = t>.9e ^n(]
+,ogt t
dt Fo.,ce
IB
,f
Le t- 48 fz .tbz tfou-,zv c-,d Bd te d{.?lr-6pOo JIEZ to*.,.
D&t-o..,c" oi Ff"F o[ ok-vafr%o
*o,,re
" $1>= 1-o-
-hl" eh e tr-vab-.eo efr +-p oi
-A-,gte of e[evaF,%
+ t"HG-
4
Jet- '6ei3hF o[ -fat sc" =12y, :: t":l.
'heftht o[ ;ole = (3, : eg.
Jfiz obu" d.,io fu veyete.frel ,P.
tlJ
^l.or'ro
t'i*{r LA -- 1o"
J-*- +'-F or-
{b- ob dt-""
-f- t.-,
rooc ludel
ta"s -
-4{jacznt-rlde'
*hht -+-&.€le
fl"6rt-$ft4a: eo".
{r"6 ga" teJ p = acr-
o,r6le &o,
01e
JhA.
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*ana = 4c
'qt
-Fo', Lo' =
)cru =
u=(
:Li l{
q
1J6.
9J3-sG
fonp = 1!1
AD
fa"' eo' = :c
I
r= ? = ,=.]3
'li
= 5 1L.o.
t_-1JL
5t194
16'.9'
= 6J3 = 6x t.+3 L
: l o.3q z .D,
-haf6ht of fouoe"
-be.!r,t eb- Fle t'
5-1.1 a^
1b.33).rr,
Let- f.?ffat{X I*e<, Ae,'gr"t ba *e,
L4 LtJ o,r!u-n ed ;tha h J6e, *ree & L'-epn ab-
pofrl c-
*d" -...oa[a bd bookeo go..l- cB, t,.'+r-,
?"roud
r"s Jo' = g'
D fr bq.,ce bett,eeo $ooi o$ -L*e. 1o gof,.r .rhc"e lf
for.r ch e,r
E".ou.t
gt* = S- ,
O"rflto ofr *"ee = +" = *c+esr. -- Ac+Lg.
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IE, a-bove
(PX.'e eL
t {o---ntPoo
,{l'otrrr.
..e3'<re''t
''" ,fbL -J".- "b
llgr''t + tvez _
CoS 3o" =
48 be
-Fo',66or cA
ABI
-!- = c+
.v3B
cA= g
!3
eBltc4: tt r I
V3 ..J3
= 8G-
G=
cei =
4g
cd
_8-
c6t
t6
E
:3=8x5
GE
LaF
{^gta
AB = 4e3lr o1-
+l.rq.te- eh e bwolftro
Jhe :bocoer cird
e l+vcthoon *f t"f
taweo
"h
Bo ba JR" $rtogy
ot- l'!du.oT d'c.- p
a=af,
> I D"...
i;oy o[ dta.?rrd$F +-D- p
P= +4,
I e t- Ae %C.r
o '|lapfaf $- =BD =
(a, .v,..
Tbe ^L-tz ,P.,
{o--,,ah.o- & we,p-er.<oFzJ
'o" 1o-' of {,fo^" ^ tLtot'L:x'>'
bilA LA =7o".
G a -fghu o.gted 'l-ta"3.le'
ft o^e- + fre. 'Bchded'
b
Ft.drt"ll-
lt^ *)
B
asgg - -A
{i"o.c elh rida
* poLea,rre-
+cr. s = o?!or i]a-^1"r de
''adf"r ce -Frr2e-
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a.Ble &e
fn
^
bec.
opportli,rf4e
.'til'o ce-t JriJa
*en * = ,49
AP
*on sd -- tc
AP
ran 15" = tO r(}
AP
lo-+ a- =- 49
&: l:{-3) - I O
-- 4.3r- cr.
.lt"'2xr "t tla,il*ilrld : :f.3-r.o.
d& i-."" tel-cuaeo P o-d qf oob of |our" : l+.6:.o,
Jeei?hr efi .rhe a&l : l. a .o . 3 cD
p &+oos el- q-1"' t $o." .[o-p porF = 3"2.q. = .CA .
ten3+r. oF ^hddot,
c':,.LteA 6( -[a1, port : f e., : EA
LaF d tu Jtre- aoq.lc lc-tbte^ded
*?"
ot- ,lhodow +D fog of ff9t on; -Lo-p qorl:
Ji., ct$o.re dc.fa ft r?,rertoteJ ig -f€.*.'
o[ t'k-'" &! lhocr:o. ,.,ftt, z4 --1d.
J-.*.. {pT. O gr&pqareE&_grir," lt="o
t oJE
to x t""13 )-
If, -12
ta^ 11
= co_
Ec.
**n = L,
C l"-'-r 3 : .t) (---{ A
4te"<*-----."l
EA -cn
a l"L
+ e-3,)
-:9:I
t'b
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-?" a geq.
*o,,o1 = *g
EA.
lan45o: AB
*,ePgt"t
4'c
,Ag = +,e.o.
of {"-.'p po.t : AB = 4.s.o.
f^ abec. .r aBe4.
LDEL '- Le'eA
LI,LI = LBAE
A.a r P-f la"?h,r
C
Aoec -
TA
EA -C-A
= <. Lco..",,oo t1^qL,J.
= ?d.
od
be_gc_=
Bg+ ,
DL
B&
=!QB4
ge
Ec-cc*
trA- - g" 't
{"8 - 3. r- - 1-4
1*8 RA
t.L = t.t"
4'8 B&
BA = t"6x+.9
t.L.
: +sm
,hcJnhr e[
!r"-ita" -F-,uao
,lePpr ot .[o-g 3orl : f.& co.
Jrefght efr ffi bt PQ-.= r.s-" = AA1 =Ber
J}.-L bui Ld I .a
(
eLl'wahm -ra-od
CD " 30 'ro .
4i"rt poi.ts B Le.4trlA.,-'LL sL
(U
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let- *,o
4t
-Ar6t a
DU;A.LL
"b
mov€J fo p' a_"d e.dz, p
eL,zo{,"a- f-o" Bl . p 6d
EeYruo.n ott""rr.,t'.o.,
?of-k
_ ,1g = At6r
a t,F,,.^t"l ,% rU 1"-.
J_A
l]
(
. >g.g **?
,15
_ Bx_
v3
= 9.s,E..,.
:c= 2€.sG .- 9.9J3
_ rqJ!.
- lq x r.+32 =_ ta 6..
Ar a-"d e.d?,, .porftfon cl,o^6e| +t
},=;€f-+t:b
'fiai!flhF ot t.rrtdfr? aLovc_ r-4c _c fqc_r
Ce = cb -€D
= co - (ee';
= 3o - t.5 = 28.5.o .
Nostr'
tof
?n
g, &-.
G rLdE
* a.' ed =
G=
=)Y
DPl.Laoce
.Ih-e
dq"'
r,!6 hr
ce_--
ae.
> 8'5
oLov- doto-
or 'ii^owo
a"tlel +".or,^Zl- i$ of .TrJr-, a,"60a &
-l-A A C&rg.
*ao3o'= Le
4 e.
)8"9
-*t
= >€.s,Q
oa:orfl;- af,rt-
*{i..ce-t ciae
.oalKe.l *o"r:r,,r.L tu.ifd p.fl
= leJQ
"".
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zg.
[.F -h*tlt o fot-.:er +e= ''l-i "q
--rvle
*ocor r
-4-qle t.( "rff * fT of Ahar{ot,,: -Fo tog
c< -- 6 90.
Ahadcl-.: be I
1' r'r. = BDJ-a^3th ol.
tl
&.A+{. D

r-L'odo- 11 (4: -t4o) .' [Fv '"
ai1le
"-t
ekv.t'ooo u F= ad'
.Ih, aLa,e- d..te ,or v e q.' .re. t
"
J p"
(t-". d1 abqo.
+-".-flt" &)e
"[ ,k-,tr,^a
re,.ctcrdeJ *4" (J e !t|u?a
Cl.*+o<gD5-z<-**J[
Lar
Lrle.
-le'e
Id-d ^ Ag
ts
|a^'6cf = .1,
-x-
"r. : xJi _O
J--- CDr n
.!, .
fa.p=
*an.:c" :
4q
EL'
.h
Jrf +o
rci+o: +fi _,(" ')
r+4o= $€)G)
2o JE .o.
loroa- = eoJi .r.,.
l--.
It*^e - ryal;C-_*" I
I +uio.r^F<t:., I
-heiX h F of
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2"4.
ffv'"
-h(,'Bh t. e[ bLLftd-.T'? . :o.o,= 48.
.lel J"e,l't e$ n,otae, atr*ut t.-1J,%q =
;e,6i''r ", tct,:.' t b*gtd% = Qttro;.o, [{"o..,
*"81" rt rL,,al f'", oh **
"h
*a-oc, x= tsa.
-*o4ie ab elewotPsn
"r
+" of -totoe.
p = s,f .
lef cl&la.a. Lefr,i,ez.' focr,r, .Q d"r.'-^t%.
1of-l =
aloavz J.,b- ,i reg' cre-t-eJ P^
at l.hot"J,r.
D^e
"t iI}. Rcl*.r..r *q[.
-tLt ^d, -1n""^01. ,i p
!tF{,
rt-
'?.
,,FL't
^,
{o.." r,h {er"
'N.- = p"
;1.roc-Jl = 46 .
v'
5t '.n
(+'",
e
(
'o^rl
*-nn 4 = Ae
,1D
-, ''t1^ 4qr __
I
I c^P = CA
D4.
=l -ka- 6o"
= 4,r rrr
-"'
. 4.,tLA = >..fa
=i .}'- zot€-r)
> ro tJE -i).r)
= )o I r.-T3 !_?)
= >Dx D.t B! .
= lf 6-+t .
'r
Zp-
:L : 2o., .
4e,'6i.r ofi -forr'r"t L
= o Ppodlt aPdc
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I
I
I
2.5.
l"r +,cQht of r^utu,stariacr f.tLl.h ,j.,_.= AB .
+le,?Ar.b ,b fdu k trd,T, = I .D. = cD
-togre ef d1.--s'L
"h -ttf u6 +-t, rr,ird. < = :o"
A-Vte ofi depv"rr?r. of tob- o, f"1r f".iLa,rn p = tf.
DPri-o^ce- teta:Ea- +*'o &ttLa,''tl '=
(>t'
-4 = g9
-ztB = 41 1-16 h'r x6=co t-e-r Ax --:-
[','nxcr ri
"- ra-4"1. fn
'te ='dl "n -t- B.n
46: (at s)-o
a.
Ix
Itr1.r, crLaue, ,!4r".,-ffl^ &
8o .{tr do,- ,b ffg*""
t?"rtnbJ
ar ,<hot r.
B F= *"
-r
.1F..,
$ L Ax&
ta":d = Ax
t-
71-
3 + q e,)
ta. ra" ^ A8=
f3)
tL+ I
>t, .
(-^
BDn l= *r=e
I,
+ cL-tg =:{- =O
) o, # * J::,1 = 4 tJ<ti)'-<- !" ti
- +[J3+r) %- +(a-,E)-.,. A€:ate = +(A+g-
(].cr [tiho-%J u^]ftd.,"^a , 4 {Jc , 3) -,
bet:,,e'. L<'?w$ff 4(:. r1r.,.
Or"O
Ir efoN"t
D rJ ftrc e
c^,
:L= aJZ --ri
,fAhF &.,"(}tl4 o!- r?-'ct..Jed o"4l- 6 o
,h
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*e r +e,"61-,r
6et"3Ar
+l.7le
-4-? tc
.tcro x - !6,
bL
ta"451= +,
DL.
Dc = +"8.. r
Dc : '-o ^.-6
{*o-' Q *@ d- "1,+r.s
ob StQ-".
-,"A}.,h
^81"
f-6 [,'lJ 1.1 aj[e & B
ol_l3l!_ rG.
€fcree-F rfl4e-
e ["...t-io, eh +og "h
eLc.rat r"c- oF tcJr! rdr
oF ordcrlol l-,e 'J..-llt
AFztFr.re = l- b.r.crI
€L
efr
At-ab?- d = eb".
F = ,td"_
th.W
JT-
"ioh
s?.,
aky.
.,1
io'.-
l.
J6,.
datn
l' r-.
+*"4?1. crr.
s- ap-cr z-,|-eJ
aJ z-Lrourg.
Lants
= AL
Dc.
fcr.- ad
DL=
=5il/
-r, + tjL
a -r'h.)
G
*,.D = .h l',.g
^Lr:) =16
{' t't x 'l:-r r
€r .l-.*'
of 3e dtrt-a L =
= o.8[-t]+r).
D,8 [.l3 ir ).-n.
.}e r"Xr,.r
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)-1 .
let J..c,khF
l^li.J ii. ol-
t)
*-atu o[
UU
l-.,rtz "ltCU
tT-
to
l.
J6Z
o.bov"
ofi 1;otozv : l-'.o .: fr@
r'lve
' lrz 'rr-o = gg .
z.b"ation !'o- tc-k "f ri"." <.
elr-"ahl," -{-,- Zo.r> &LoaL{ JFr-
ti 'Y''1ov€ r F
-- ao". [{,o"^ o'1.
dcrt a rt reprrrr.,t'z.l
d* "| {.3--' c.r a|.,ot,.,.
#qt* o,rgt.. t',"ar.t . i^n t-',9."t*del tc ,$ o' .[ko
e o" [4-* c]
t.6"L
5. A *!3c'
*ctn a* : ,48
tsc
.la. 6oo = 4,r
f-, a *oe
fa-p = ae
DE
ta-.3,.,"- -1"
:Lt)!
).+ 2ll: -l-.li
-rit:,
>L
6= x€ _O
f" G :+ Er2o = x€xf,:
? r+2D:3a
:? lx: 2p + x=lD^r,
.-1.i
= xG: t11;r{1i = ro6.o.
Ae,ogr.r €l -h"a rJ.' : to.e.r-,
ti.ltt
")
r-fvay x, = to.o.
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.
2-8
fl
tove r
r le fehl "h l>ur-tlJ 'P.7- = r ''n = *6
+ferftt f et- c-able totoc' : tH''o
- aD
,-t6a.
lrr
+-<le o$ el' q,lnoo^ ,b a"p u[ -lou.,'., -{- o-- -t op
ci tril.l'h d=6a"
-A"glc "i dep.<rrf--r of- tdro. r,
iof + builal"n V= +4'
t,cr-ro- l.o"t
C
o,f,r.,a drrta & .'- eg. e-re''feaL
{*.- of {i€"" ^ 1l-"''
CX -- ' :t'..
cD: Dx +xc
-LN A ADX
tan qs" = of?. ride Lxa)
-Ac{j. rtde tex)
!' z axc
1<ro 6o" _= -L c_
AX
€-a +
I 1= I J:.
= 'fl(i *,).n_
-Foc.:ro -- =+f,lit r).o.
:7 AX = I "o.
"^
tnl LD --
:
x'+
q-G {- +
+, e,'gt"t o'i c,r"t,k-
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Z1' Vfwcn
+k,gbt oh I'br,i -Aot.ra = +8.',.
-Agte d .teg'.rsio" o|- rl.'g I x
-Agla c:h d.,fr?rr;o.
+
ahf€ z P
IE obo,,e Jala & rg-oe.;73
f. j *.". "il {,ft -".e a.r &l-,a,o .
LLI D, f a,.c. Le F,,.x e^ ot ,?. t"
':J .o = 6.5.
= ,48
"for"r
-*-U1n f$ o.e
'b.r
Iu.1eJ ,r11. ,'c o JF*
^
J
-+. F: 4s
c-e.
+c.- +5" - +g
EL
Bc -- .+5 .
-O
/a C) /-
C' '" (rj xt +5 = +5.43
{ = isLJ:_)
- lr r( f-oicc te F14a.. th."-a
I
)C .')
- +5t.4..)
38.
+'
Lqr. r
_a^
oi
fcw, go" -
rcB.
+5
x-r8c.
FE;.=-.lli.'ta-rar| -+df tt+ rJaz,l
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30.
+^3ta e.bt 6'f,;en
"b 1rp
-Lot oar : 3o'= d
"
[r ,, o l-,."o. o
! +r;g
6ufttf.? = a""=p.
+
{o"t
-'t"gl" rh
{oel of
Ttr! abova f'^
1".,-.'otr",r",
d,"fture o,r lhoc.r.r,
-4" aAe,D'
tc".r
lts =
-Fo..6o'
=
Fs> -
, . _p".
?+g
AD,
5!-
8D
5a
1.<
{n
3
"i
.'t
-tle&bf of to r,-re
" = 5D ro.=.48
-tte ."or-,t ol, t'-, i t'l '"-9 = t -ry0
= cD.
.7- "
,bFt J, ,'..-o /, il, ( p o[ JLt
,or I tL,- li^"e -- c,r par +- l:.f"]
| ;",."._k"&
I
1"€,iH- .'h toi l.l,lU =
-ra CgD
+G.c(: cD
BD
Tar :d = 4
5o
G
J-= 6o r
rlz rA
=59
3
of 't.,,'- 4-o-.
tc-'Ed r!"
, 6, , r
bLrL rd r 44 +y c)6
d"_.^ "h
3.t.,JeJ ajL
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51.
-He ig hr
4.2,e
-Ajle
6iwz', bo^ks c,'t.- Do qgpo,r?E ef.1e5,
Dr'r l-.a" c<- lxF.ure-, t.'.'ke 6,s-= qe*
,fh. o.bov e, i.{o-..,oht, 11 .,r e g"re r a-f6.1
S +"g*". &i
+
.t
oF .I6c, L;idqe, : 5('-1. f lte)l.
Ae-t>.n e *toa g$ L^- O ,a i. .- c( = zo". le,
d eq"r err.Ioo o| baola- 2, r'- e p = 4a: le)
B.4.
.ttL {r'--
^
r'oghr o"^9l.
oh -[-hs i'rcludaJ
i[Fa o
ll"ot -,o.
_{-,t.
<ltoof-, 'tJ
( oaz
a9
3o-
-
B'
-r. A AF,n
J- aAge,
-Faop : Ae
BeL
f""4S = ee_
BBL
BB,: fe9
JoG t :<o
solG+r)
*an <o
B,e =
AC
B,g
-3q
B,B
Sofe m
Brg. = ai8+ggn
-D,lc to.,
" Lr kr.r^
|
#.o = opf ooil;.,"a.
- {
I +uincr"l r?& I________:=-_ I
h'.^t r = 3DtG r() r{)
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3.
Le l- $c^-,o pot-
G a AYe
*a. < = AB
BX
to- 6d - l'
-
,q€ a
Ag:-.D
CD h€ ak
U
aciu ret +€ ,bh f ' + '
f>i.t tct"c. betcue ea ?ole , BD = 8o .o.
kf X !a PP.f Letcr.<,t -lbc -e f'. o,,. 4 -2
- A-,1{a .,, e [r vahfll.' oi *+6 Le d. = La"
-A*jle "i
ato vaffor o[ co k F =, -"
pi irr*. tt pflor {--". Tolz'ao' ='BX''., =x;
pir fo-"re "6 3"t 4'o''-' l.,la 4-p =1Dx '^' : i$p-r
'o
llv oj:>o,te Aclo & ""P"'*-t"'r ^
I
e do'- oi d,!.,''e "'' ^*"-' *-i ,/ l, -
i- ',iu' r''""^'rr' t "' 'i i / i
Fa l^"t',at" ^€9-j- 9
.F'n f1^"s = c;$x'!-{
iai"^c"-rria''
s^ acxD
fon B = C P
' lo
-tc,- 3o' - +r
go-f,
!o-, - 1^,.1f
*6J-, = >LJ3. .'-6
'% Ci =2 Bo -x- - x.r: [-G) :> 8o->c = 3x.
+ t*- 8o + x: 2-D. $- :oG
.l.,e ,!r"t "fi g"l ur = 2 o I: 'n '
l> rl tr"ce ob p. I- r fo"-- Folr- :L : > o '"'r
Dior-fcr,., c. o$ Pgt f"o'. gole -:- = ao m'
g 1- X (€o-2, D
+8o-o+-.J
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I
I
i
l--*-*----
,35
| 33.
4. ,"1r.r of t" , e AC -_
-li
A, -,1" rri Jar.',"ri,L
-Jv{
{-c'la oh .1aq,,11P6.
J!U
g,ct b b.re nol, ^
B'
'J
-t,"r,,^ I DlP. a ? r )..)
0'
ta. 6c"
€
8,9
= &q_
B'E
B,B =
B, 8, -.- B,B 1.e8, 1
-{eaf 4 :6p'.
{ezF p = 3po.
20 .o.
oI gJ.
"b ?"tn
c., te
L
L
: Lt,".r1.9.
"h o&e" = BrBo
= Brstga^
,q, obcva I Xo_*-,ot,'* ,i q
YeFe!€^t€J ,1..
{""". ofr {g6*c
Od Al-,or.,o.
i. -thr +.,1" , i{ ooe
c: oDDc([L atde- JJ =-
hc.-b rtdt'
2p_
G,
Lo
^F : A{3
8's,
fa", :<c.
= !,et
*,
B% = zoG.
29+ zol: = 2o I r,+z'1
{1 ' - l"--lL .13 J
= go ,.,.
r/3
= Q-@-.
3
:€o
G
^tLl+c, "b
oll-,",;,olz,.
o3]'or i 17- I iJe't
of ,"-elu.leJ a€t & 0
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3L.
. 4l rw€a
0
rle,'4lt rl jtaa,tl-L[ = 1.n= 131 .
- ( VU
"{e F +-e,'5nt cl tourc" = '.. -- ag.
-4.gle rb etc vr"l tin o$ !o-tr;o. o[ {ra3 r badl
-A.-qe ob r {e vcrl-r"cn D]i +op "i
.t la3 rta[_$
f o'lt "b oka..va F rgte., to- ' p,
fi" oto,^e datsa i lrep^ner e.,bed fl -l*.^
of qf ,'g
"."e dr al,owo
J; ',"9t
t a',51" **r"."n3r.
Jtrz Frc0utde d ^l?t" '1
r----- --- ----
It,."rs = erori'l-r- rt;, I
i -+.rl^ca^t rPan, I
fcrocl * 4g
A?
*zro,:o' = {t
A(
-Ar= r^,J-3.
-6)
{-.- @*@
*Je: -h++
*'.lr-]^ =n
{{Jr_r ._ I _> q.
.i , ra.,
trl -j vr?,
= +r (e+t;
= B.r[d. +rr
z
"1,
-l ou-,," - 3'{ (Jr'r>-.v-
*= 3oo
F = +50.
'91 o..,.
O -G-.
Jr
^-P +L
r - r]t+
AP
4r -- A F:r i _^' l--/
I
i
I
I
I
I
i
I
I
I
I
I
I
i
I
I
-t,.'!r.r
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z1-
Let
-Le 1g+r, "t
llado,.r t" 'a'-
be d. - i5"
le .,.r1r, dr l'dot: t-'?t t I c
JV
o r--d
lua ntliFuJe ir 3 = 5o
|-t +,eftt,t d -1o.-" Le
k
taa,I
'- 1,rl-,p- :-un attri't crA z
= gD'
(r x -t a ).o u'lo.
t'1"'-.,
= -18.
-.F"*..,fuJ ,P.-f,h-e ct tor,^e
tf d."g.."e
,".-'
{o..na hote-
or Al.pcoo.
i^ "'"S^t
-1
"'hr3la F e
+ rr.,e
a?31€ Pr s "[[ie o
- TL*j,b-4i4s
A,Lce"tlt&^
!i. -+ec.
-l,," "r :
-fo ApB.
-Lo-' g = t11--
' {azr-a"j €r.
ld-to^ 3(] = -Vj
2'7! a-
L't-t(1 ": t€ -o
-tr.4^o
-4+.
B. '
=4
a' 4)
o P., => zxr-h = *'Q
+ J- C€-{) = 2rt.
'J3*t r?-1 I
: 211J3 '.-
't*
: >c I J:'ti;
.1.elght of -lot"tv - >cL.Iar,)m.
,( . | ...+e.l
*=f5"
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t-
3b.
I.e t- AS V +4AbF o[ t;oe L
po,'nt c cr"d tog -tou cl-,ar $.ro*nal
-4.,312 -,a)a l>x %e o==o..
Pf1tra.ra +r-- {oots o$ F'.o. *.e--
Iouch.r.
6vou.r = io..'rFee -
.Ap
.-ifu o bot,e ' ^(a-no F,"n ' rl
J,%u'e dl al"oc"n.
O
,he&hl- ol I'ee = r4G: Ac+rB
{v
: Ac -r- ag
t-
a"5te
"ftrt +xta, iL "* .fi-
Pr s irftn
LL
aF
L-(
^ll1
token aF
3oi. t- qzl'.e.e 3t-
BrF----_.2rofteA
tbear&
^.dft ",...",
f6y1 36' = 4C.
da'
tos:o = 4€l
Brc
Ac : -!-!l'' .'),
G
.13 - tn
=- -g'L
Btc = !,o m.
e
= .!-L r- r',
(3 .fe
= 3o - roG.
G
-Ag = CA tagt
Jo.o =
opr:<rri F alde
'Aclt"ctc
ant sr"de
+,e ftl r tb -1"2" = l oG rn.
i
I
I
I
I
I
I
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.5.l-.
Lc.{ tr1
-A€tn
si.6 = te
B(:
*re t'q h I
0
38.
-r-'aPBht
+nte
4n,
Sir to"ce
'tfu &bara
{,"0** 0!
f- lghr
ob c.lble co-rrctzJ to Lat(oo.,
'f fqr t Sa Fr?- of c -r1. r.rtJq
= Zttr,,lad
CYoL{.,d
=
r.6'm
=
-'4g,
r( - 6oo'
lleftbt ofr Lcrtf co1 {'o.n 6ranod
,[C1 crbore dala Pt
{ {?-"" or 'thcLlJo'
J- :rl9 r. F t'-"c."5 t.
i. cf ul e a oo3le ir s
3 {"..^ "r-
-7rv^1ad g lU".-"
o.€ "h
.6en
=> 9- $- + 4"=
_ Zt5
4 F,attooo *,"-^
0F 'trft = Bo-o = "rB
o[ elcvah'm {,o.., r4o.] J_, cr :
o[ at-tvnhntrr .J-.r..,
Man:, B :
Lttt^:e,e- *.co mel - M,Mr.
: AMr t 8F42, ,
l";[o.-..a t-,oco f, wepve re.rteJ
{hoc,ro ,
oogta t-.ocr,rglc sba o|, Ol.e
o.'.'21e ,i o .[{eo
1!g = lo4.5t:.n
2J
flroctoJ
: lo"i.5.&
"r_
3so" lvr1
6e lv,J
3q
*&o = "tf*f trtoE
.roo* it-, *",d. 1
{a.{fil
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40.I
foo or =
*Ln., 3c" =
M1B =
ta^p .*
fc,6o":
8I,4,_ :
4u
BH-
g!
BM-
go
.J3
8o.fe r go _ Aox a_
{3 fg
= iie€ "*tr;.r,3
3q. ler
leQxr ob pote. ='-{-'..' : z,r-tr'r a[bttud. $,.,_,, ground,
Ie.,g+t, t:b ,cl-ad or-. ba '-L'
Xivr" trr.al- -L - t-.
4s_
MB
So
MrB
8o-B
M'h,L = Mrg+ BNa, =
D,lFo.ce bnh,-lee", noeo
+*A" "i e0e vcrh"-'
lfu o-Lo"" dort a &
ob {,"3-* zlJ d hoc*o,
taoe = 48
BL
cf -c..1 athglcda be
rcp-rereoled F, (o*^-
:- 32.6
.6
e.
r,Av
.1. -iq F +*"^..Sle &{ ,,,e_
"f
i-c[ndeda.6te&oTLeo
pfFcuYlt,tide
I
-t-ft1'a c €-t llA e J
:| *ct.,€r : :L
{.
_/ -rnnF __ _Q t" +rr. f]
:* O= +a# l) s4go.
ch {rL..r altrAtrde & Jeo,-4.oVIt
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An.I i -r
:Ann le
{l
-As
ob
ob
Le trL,e LLatLA P--a .
clr va hoq, {,'-- 1Jr^- F I F,q ( *6 t,.r,.. r]
eLtvoft"o.r *,o-, por% l- q I Fi.re. _< Fa l-,.o1 >J
q = bo".
F=4;1
D ir Fct.'tce te h-.,e<o F,?alt-oria* FeL = Zok-.r.
'I[, o,Lo,te ron
{o,.^ah'o., & reg"ercnt-ed
ff tj ".-""' "b -{ i6."c 01 r hog.,.-;
]i -pr +.'atu q w "'b JR.
"?. 8ce ,I[po
X
to. a = .,4s
A?.
L&.6o : 4A
*"
Ar = 4B
v-e
O"O + : -ag /t*-,|-e.
,f2.)
AB = zo (z
(,c -r I
-A.rAQ =
ft_ a,a
20= -€(]ri+) +
.<l-,o utd dz^d i l-{
Y.-r2, L.-,.
to-p =
*n-.-1s"
AQ=
AB
AE
Aq
Aa=
i;$"* = ro.r3(J3-J)
=,p(3-Jg
lle = lre . tc,l3_f,3) : 16(3-r"+321 = |z.6tL-n
= lO^ O.-r3,- :. W, +"32,L,.= ro (.t-r){s
€
Slah'{:rr a
+n -kavet
f e o.- zl.-d {r; , ,.', !,a *c
+t.
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+1.
fhr'ght + rhip f"-"., rtzot?., .!-evet : lpro = -Ag^
-tlr'te 4 ele vcrhoeq
"[ *"f "b .linh o(
= tg:-?+"A1" !b dtp'.rct"r:^
5 6.16-- of (t.f-6$, A =_ 3d,
l'ef6r't "l ct3$f 'co = 'r'm.
J.'iLa"ce,
"t- rl",'1' -F.o-^ +*F .f t-q:e'. c-t.1F.
ne,ir"r .l ,(,'-$i
"[.^:l? ,_>..---itrieo -1"e..",.r- -b cr,'ix- = p1+ra _l >:o-_- 00-rarrn I c )4'o-l
:
aloou, do+" fc ,r7,era-t.A l_----' ,
'
': d.* "l d.ii',,. ot tlow^. D---------:i3
-?,", ,r!lr +-"ci.6le, f{' ,r.," cb {Fa r".ctu4s.{ ang rL &
e . .rr-o.
f*=;- rFtslE;-Ad.'aeu
"Frid.
-Lta^ +t" - Cr
AA
l: a
AX
Ax ' ' 41'
".t
*n. 35. = xp
Ax.
-L = ro
v3 Ax
Ax - r o,,lE
L. - rtJ?.o.
o[ ctr'1[ - lor-ro-e = otJ1tD.D.
f-rF..rr^ _+ f-1- e rtP65 = rce.o.
Jv,%'.t
a)
d fi t a,"ce
t)-
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+3'1
-i---
142
ir
i+
l
l+I
lorI
l**
l
+2.
-t-|e .!rr
r1"6la
4'xylc
+l-etht
D&hr"c"
+le it3hF
+''llht,r
Jq!
.l.
tre.,
"b
rhfp aLove u:,iiu tevcL = 8.r' = '48.
of etev-h""h
"F ++ * ctffit+rtr1 a.26r" .
of -lzp-tr.oter o6 kf,to",>
c'f l"ft{ =- cD
tr h'"eto {t"rop & }'itl = AK.
rt 4?Lt a tove- r;'og
= C_x:'Ar-n
ob hirr = krrg) ..,.
l,ftt g= 3Y.
*a. p = xp
A,r(.
tCtn3o : g
4"
Ax = eJ:
C
X
tt6ov- de*a F,L ,reyerc,:ie)
4o-- o$ dfqc,.... ar tlrltu",^
ftrr+;u6u ."f c.p,
"$
r'oc tutdad a"6lc- 8-r o
tc".. x = 4^
-fcr,-r oo'
AX
-arr.
AX.
A
{-s
-Q=
",3
8Q 9 .r= 2.1 -o.
A( = 8G.n
+,ef6r,t ch otf1tr'9@^r"9 -
-Dl ttt"ce l.ra Fr.rt c^, 'h?tr e <hP6 = 8.f:'o
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:4gte of &p'"srio-
"fi tf of te ".pte z,
J-e fo hr ol
tv lc-.,ela r [$e) = co
-.I-
ot t"n-"-
"b
z CcD =
r"r.,,^i
$o =
rr, .a.
Y eF-' er e.l-zd
a! rl-'q-.r). c
o.ra ol- l, ,
l,] --
d'Fe o
D
* = 3oo.
F= ed-+.de o[- d aPvesr rqc"r
-hefnrr crh t..^dz
l^lfd +'. sh #ve., E
'ffu otbore- datFcr &
,i {o'--" of {,96*'"
3" -,"grt -*1. ft
L
t ata r( :
'lc,r 3o
LA
AI
C,X "
"= tZCx.
= Ax.[i.
Al("tl = ->
cD=
l,J icllt,
4.,%trt-
E(e
XB:
of-
ot
48- Ax
t..-pL
i loa
=:-|-o
:6-r-')
3
- 5o- Ee
3
AX
50
{)
loo
-1
te-ytz z,
fict u 6 a3 ag"le ,1 s,
f&., s = t:P po{flL- t?&.
"4djac e"ts < Pde
*ctr g : 4g
BD
-tar 6q," : g6
Ct
cx:5c)----E-
v<
F=ao'
4^t.e gD
= dx, (]D > gd,
l
4.1 .
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+4.
I,ef -Ae'5rgj2..,3 +raqctt.J 4'o ",-. A -!a
A.r3le oi etrvaF,$q ob ?oP-l A d. =
-Aoqla "b r Lvo troczo o| ge,? f e
J"ei3l.r o[ ae"opla..re. $.,- 6,.,"-J =_
D&|o,nce {-"6-wetlcd #- tg recr:48-pa.
6cl?0-.t;;e!.
Ai. -_ ge
B.?
+29
t q .4 ec(.
'13 :
t+Lt
._0n,
"t
&"4ln
velocl! (o- r -rpecJ = -lSrt-n-ca -o v. rt-;
1t"^.,.
&bov< c{a $a r! vegvalr-1t'e6( 3 lo'.-.
<,hr-. ar {Lorr',.
.,.h;t I .r'2,-^ qlr c>e .l yl a
-.1 J l)
(t O "![^,
*.'-ts = og?.?tr 4&9
-{a ce ^t-riaa
*o-- < = AR
XF
.la-
4e" =
XP=
3Q. =
Ayeed -
Sooo
xe
3DOO.,-r)
x q - xr
FA
3". i.,.tel
+o-p = 3q
xq
ta^ 3d = 36rp9
xq.
xq = 3ooDG
5OoDL/31) rir
Sooo LJ3 -l)
- l5 -
zcox o.-1 .).
rqa.
1 ""lL<.
2oo CO3r)
/,yec) 'b -*e'o;fo... = t+a.+ -.A.._
+e
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4t.
I'e r
*^gla
4,13te
-4,'oea^c l.avatte) -{' Dfi 4 +o g
,t
et+valrbpo. ol pogt A =
u"
at-a va LtL- oh PoP^t R
"
4
g
t,.h
"i
-6D
FQ.
A$*
"h
itAc n
=1- 6,".,
rle
-Fo^F = BC
xQ
la" sd= t
xq
xQ=€L-n
= JE-r= z
u3 ,f3
-t
"l
lo r
6ox6r>
zo{-z
= 4B v.,-.
-- Z'fz x bax y
Y
L^" lt .
4"&t"r €b ae'o3a.re {*o"o ?x-Du'f, = t L'n
.D&Fo*" -t:-atzatlcd P" to LL( =
.ape e.t -- .} ter l.a oce -+-.ave tt e.l
/-l,Le .
JFJ alxn
"
dat-c' t% r76ra,-,f221
{ Pq",'. ou r hcu.-r.r '
5" -,!1xt +.le, ,"tr o'e
'-[Ec rsocluded o-rqlc '1
o.,
o- oFpcfF riq4s
-Aajac e"h siJc-
faov = Ap
,PX
-fa,-r 6c)- = A
P;
Px=
PQ -- xe -ex
f-peLd = ,Pq
-lP.oe
fee.{
-&*oylon" = zrro6 L" Fl'.
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'*B = 4,ePg+ o$- to.,:.'" -- so"o.
c)^e-
+ F.,cl..Ja4
*a" < = A^
Lx.
ta^ 4" = AX
CX
Ax = 6-1.
.LLA^F=
*o- 6o'
gD -^LA &
cD = g(.
+e
BD
=5o
BD
5o
.4
Ax = ';n
=
-r). : gD.
!1
cD: 'q8- Ax ,- Eo- 5p
a
= 59te re)
.?-
5!C&:p
JG
+'e..!1t"r
bi ra,t.
"
DF bt-uld.q.,? tpol"l =
$(:
_.i11".'r
tel'r.,'e-"-, pota !. *oL,:r. : fq ,-.. ^
cr,: t"zrlrr an V-Va.",fuLpae)
-A"3le o!- .leg-<rtro^
'/odt( $
Jep.zrrt*e.,
tJ' r,.brtze dato- &
{ fr*'. al sLa'oo
il-, ,*!;r +-Po^6t"
o.rX re P-c o .Feo
d *"f .f Lna,."6 N.=11".
'b tptl.'.-
"b t'-?u-t'-U p = ed.
.oF..r..,t.d ,"..., 6o 4 p----, oh
l+"^" -- *"*tt- rltT
I 8."',-lr-l
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t+
'D lr hr',ce &fc.ez. *< cet = Oo.n. Ceol.
+"Ehf o[ ^LLE)a]
tye,c, = 80 -.-',. tcDl
1"; {e.'ghr o$- F&rr +-e-" ='l-'"- LaB]
n.gt. o[ JeSr e-lr fo-,
f."
r-c.,"} t*."- top
ioy a = ft*'
=$fL a,,rsve r,o^
{o -.-abfoo & t"p"e'e -teA B
Ctl {houoo.
t =,!c.r +-,}.,Ut. 16 o^. $ Jk
r.Xc(uded a,t 14 $e Grv
Ln^O : cPPol' Lc lt.le,
"A{io c-e-Fr ide-'
.'tort C* I Ag, Cx _ BD = 6D-n.
x.B = cD = AB_aX,
to^ ". = _Ax
C^
I
-ra^
4s"= AX :> A(:6D.q.
Lh
Kg -- CD = SB-R{
: go
-to
:: Lo rn
fu;- 4:".s r,..
{*- oh t,3q
I
.. I
at
I
I
J=.
".!,lr
ar jgt,t
&om
2D.o-
$
+
Jt-co",d t*ee =
tY.* tee- =
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tc.
Ab Le fbe, ttee b'o^
-{-ro- d&ha .'ca '@' .., 4o.'
( eoi h
.,
trhr
Ine. f"al uJel atqle-
f,L o."
D
14e
d"",-, Ax+ Qa,
*a., < = Ax
t-x
Ax
atb a .A colB
r *e)
F-+t#
qi
AX
x+t.
).1 t,
Fx
.{z t e^
T
J-^
cDtF =
ft&
aDt ( I j[+&
IC.T L : A)( coF,(
6*O
=)
-t6; * f:c+at - ^r cr)tp - Ax.otr.
Ax = lb-or to-<, ta^e
l;_r-^F*
a?ee- ,--A.ogte of e-tr1oq.'.',,
-+.q le- ofi e Lr.lau"c,,,
,9, .Gr,
ItLo
l*- x aF ?oBt r.
d & ta"ca ,b, .., 1-c,- X"e"-
Le p at- pol.,Fq.
a-bove- do,,fa & .'-eg"e.Le-'lad
P
h {.tA*"" o.r rhg,(,re.
.rb!.r +-f,-"?r!
t
FHo eBF> a,<-{ X
+7.
DPPDTf L- dfde
-4d fo. c a^t r Pa.
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+lerhbt- "h verFfc.a[ toure-
-Angla "fr e[ewahL
'b -bf
-4€1. ofi eL t -h't " o$- top
frv, abw. ,1{o.-o kq.l ,}
iiT*"e 0r. lhc.,o.r,
i4 "!r"r +-,Lgt., o." o[
L9-aludeJ c.nlL .!' s, fu"v
b'cr co Ay _l pe. ,
qa = (eq
-!-I Or 45" - _a r.
^Y
Ae = .4y
-/ rbr-+o =Ay.
Lr
= Pe.
{ro-o X, o( = !oo.
*.+-" y 14"-. a[,ove, *) ,
P -- 4so.
-t
1'r €1e -t,'J P. +.'_ o
h
X
.-4r)
-
+o.go" = Ig
Pr.
Pr= bn
G
P0-+o=pc
€
Pqt€l) = +oJ3.
zD€LG+r) -. zoL3t .^3),
2oL_: rrg) ..,.
r 4.,0 -_ oppol'LL Jld.
ta-Le.tf ltda .
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lo.
Lc F c-lc crJ be- cr l- -l-.,e ."gt-t-
.j""-, lat<. "levc[.
F.r". porb^l { 2ioo.ot-r
I
of-' ctavoh'."- of, +ry 'f
-+-6le- ob /ep'e<f"- ofi-
$e". Pe - tre' d-.n- .,q,.1
-Lpq.
Jel AO.'f .- Ap.,z'-. y
PQ . lhr >)-.' pq'=6*,.,-rrj
?
otove
,
dat-a ,? t"p,.^r^rcl
{r^ <--', oD X'b"". ar (Fawn
5:^ -b0..,r +",h^At.
on5t'. &e ntr*
fan rso = Aq
^Y
Pq
crloo'.,.
cloc' J
!c.Ao,,-,
3".13L
-Ga -tcr k c
x=t59
ty€t kc A)e
r.; ,_.nt^.
c.1te-
:) u26g= +,
"Y-)aLr-t,l_-r)
i--.,ee
#,^A xO $ . -- 'L*:- =)
o.lA8 +
{ o"4<'-- 4_e' = Ac*pp'
AY _^Y
* Aty = >.-.r C brx)
: +r z7_.
+ aY = g+,>x ._@-o
*L' = >x
5_oo o_ =2 -igl
>scD
t I3(r.83)-.
I
i
!
1
I
I
A.r-,
r630.83tat2qon
43oo. g"'"
-
i
I
I
i
:
I
!
i
I
I
I
I
wep.ere-,tzJ
r
"l-'efgnr o
$
a to uJ a.bova la bc
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Let x be, fo,%1
,1,, .., e t+er
-A-qle rl rL'.nlrbe^ o{ ,louJ,J v " -t)
,A- ri' ri Jer.err,"o., ol rrocrclrt$
-f,aiglr 4 r l'..d {-o-", 0r.kq-
Pe' Le IFa -€flectpon t6n
clo.,,-.-, xA -LPg, , Ae =,r,..,,
D'il o^.. dl) rrottJ {'*v
rs xQ,
ta^ x =
O -o :-z L
u-^F- to.,n = 21,
l! A," q
Cas c( =
dqFa & vcgrcr <-^,tzd ,: 4.-* + d Jgu"c
5o 1d1q r
.L
L.rsP : 3Qr
e.
+-'P = l-+ >t th
'B
-.
P
orLove- ,Lake-
{woco y_ : (.
* eltc cl-,"o.r 3" .!-ate"
'p.
-FQ.
Pe' = pe
AF =xt1 * tq,-.
g'f.t $ oLre,rr,^ott$.-.
Ax- 2l
.to"
F - l-o.a.
'tEL abovc
At l,L, q-, n.
i- aAe*
.t
,-"x = {-Q_
A{.
Qr = a<
r(
-{D
<D
,41
ln
Ai-
xQ
XQ
ABc x
: -21, Au x
*o-p_ to^,r.
rh cloua -f,.o- gop"r
"f oke.',a,hL
: t-'raca /to"B- lonV.
4,1t0.,,..
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53.
5r.
Ur
*k
ra t. +. 'L Ll Dl aer"D * roltac€
! te tc_wo -.,ttc I Fo.rr or
Jfu acvoplala. XY = t ywila.
-A.gte eb cleg;e rr ic," ob K -ir.o- F ' x.
,Aoqla oh .1e;'err '*'" ti Y 4""" t -- p
.fFi above da t-a- & "reE*zce"'teJ P" <o-- c,h
d .fr*". ar t hou,:o '
5., vrir'r 1.'ia-"31", i-6
(!),rO
."1 t, ( ltvleA oagr. r q G)
tc,. g = cr-'p,lflti] 'rlJ.-1-#
#jac.-t-s2L.
-tY o.ri
opr.orii,z-ll
t-ou'J.
liifa +
-Ll+..€J .
-r^ -a Px Q
I Ct^ ,< --
XQ=
D.L
.fi"^
I
,r. pA y
-ta p = ro
aY
qY = Pq.
+,'"P
!Y - Fq
F&
XQ,
iq
_t
YQ r 6Y = PQ
" !A ?
*a,.a f-F
PA
rq l+gd-P-lL +o.,... t-pJ
= _1C.l4-
l a"F_
to'a .r b-r- p
ob ae ^'oglzroa =
4.^.: t ^.E ,--? ln"
lan< + fur"p
1.'" P
-l^,e,%t't(j
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54
E-A - -o--- nA; pr. * l^,,"gr^r- .r *e
-A^gle- cr$- e t"va tic"- -f
-A.-qla ot= c L"yo Ffo-, ot
&. a[r,'," L q*.-,.af Pr" r1
{J6".ve dJ ALot:o,
- - r)DDri ( i L! .lL de
" -) !-
*liac e"t- eia..
C- v.'gr"l +.Jc'"gle
h &€ ob
3, c [uJ eJ o"1t fr ,s , .Ifu *
'i -toL-r". +e,bht_
B '4-c'". P="4
I 4,o- c =F.
"'.fY cr€.-t ed I {,r-*., o}-
P
QX.
+B
4e
Qx.
D'ao $x -! -AB
54 t@{
fo,"p = Bx
, 7q: A-t,4r=
--t-r A BFA
tan<=
= A6-a .
AE
| - r.}nB
o- tan 4
-ttrrr r{
-ta.
Qx
+ to"p= 4 8- ,4x
Qx.
916"13 . *R -a ^| _ -{rl
Qa.
e=r
ID 'aF
a=
AB
-l'e,it"r ob
DIr Fo.rcn t{*
l-A
4e
.t
rola -h^a-
----- ---- 1
tr. < .
e>r:49 =
ta"x
o
ta. x *14^p
po." = o**ltF.,.^r_r"^u;
porF ! tor.'zr . .lf t*.",{ -lonF),
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51, Lef {e N4 .i-aAde, '".i+i-U 1
ah
d fo fi'rou"d'
r".ctP.ol-.tr-
l!i',e..' f k {oot. ft 1xrtldJ ffiiesgl- J&t-a"c<- 'cJ
lc F BBI -
hl .o c.,rJ Aal = 't '-o
Dec., a,"6lc of z Lvze Froo" S' '''" et = P'
{. aLorc, r%
{o"".,oFrqo.' & n- eg' esc^tcd
qf sq u<e aJ {oc.,o
Lel Ae_I
A<ou'n
A'?=* BP=
f- aaee'
S;n c{ = -o
CO.go(
g a rie'e
E
-o
r% tro"..- oh
Ag = atet
L
de
'd
_l
Jt"^g = A? * ci^g r :r- _6,I A'B t Ag )
cor p = B'P :? cl]( ts = ,j *S _@
" -FB' ' +ne
si-',a. g+
AB
Cose( = -!-Ag
sinx-s,%g = t. AB.
cosg - colca = 4-, Aa'.
co!E:
's{_ = a
3,?'a -Irbn p t
AP-
Ae'
=gAB
o*o
@-o
/=
-e,
-@
@.R
e-/
Co{o( - aa{ b
Srr)p - Jl; d
+
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55' LcF Acr!7ht c$ *t..1.' b" 'l-,'.n.: Pe,
*oVie o! e Lewcr lL"o.' crF loEF A o-'
6".oe.-J
l-e I B k Tef'L
't ''.', aLo'e' '!r;e A'
a^61e, o$ Jegv e-cr r'cre o[ -$o-t- o[ -to'"'v
Jft:r- crLo,
"
dc,fc' tt r7 erenfal e' 'f-'-"'.
a! I Aou'^,.
j".t.o Bx I pe. *" ". {,"7.-"".-.' T'?
- ax- b-.,-lrt A. FBd
r^ -AgBx
lana . 3p
^ 1..r^8, @:-
BY("I O*'_O
-tr6rr, o e,: p.
ob' n.V,' "
o
@
56.
t""F
=rQ
QX
Sx-tg11 --
PQ" ll(r- Lo..6a..,rl^
-.-FrcrnF
.A e
'ocl
c -t() -l) 1oare. = B. tc,^... r rrbp.
itaf3t"r c{ ob{"",ra, = AB = r.s.,..
fi2,6i-'r Dh tor.,e -r = pq, = Bo.-.
+,e J6l-, r o[ +oux" oAowe JFe, otce-,,ro
D & i o,-'re, te lc,,ea.., tocoe,. &
e Le orgtc ,fi et-t.-t''o-r of
Sli alore- daha 11 vepere.tr:J
ft {o'- o}- ff?- ". {hqrn
J...- {J? tcr.,o = ofporil,- riae
A$oce^F cide
ot'r. t ,r, -,
e1e : 3D -l g
Qv - zs,s.".
xB- = z*9.5..-'.
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to^ e = 2g.s
4d,
Bc: J-r-?+i,
5#,0,r'= 4g .+
BL
=I'99-16.'t6';= 1{..
q{'
a :-i.f
*
sl..,a+fa-, = flo
5t L. r -ou l>z hc fgtt
lan ,1 foct ErJ 6a"
Let. P *Q te e4u zzL
Jtse aLcve, r'-
{o-..at-Po-
{ r'gr*" *-l t[-oc.ro.
e[ rFe-l = t.s..:.
q,ita.
?*oL.--j. .1f a-,
cl 9r l,E",c-o -tt-e-( 4p = f).E .o , A6?:16.
1L vag-er.^1,..1 g 1.,..,ob,e
d..o., ?x s- 1,4 / QZIA A,
-!.eq
(
!5
BU
rf.3. -n.
I xq LCA, zktJU
SL". b3 = ZtA
LV
cz : 'J--
./:,

cz -- L.6q'+ .r,.
ol'
u
J:=
t
a
r.5
15,.L __
(3
#% eo" = x11
{L.
=) {c = 9:5, Eazl
= /.lE v I
[T/ 3
v-3
%
l. 4 D'l -l .n.
For bo1 r.
Ie"r ol rF..'^? rs = roo r..
-Y' mcrde t.4 tl-iU
Fo' bX.
-h*hF 'b L-?(ct'-?
/ ta't
6oa J I
i
ffoLod = 6<"- 3cr'
CD
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le- "r,oJ
z. ty ri--'.lX c-.rf tr', b..fta,%? -+o? F-- 4"'
Ie .144, kf lt ,fq--.zal eh
Fiht .r'ee t- rnt'gts
ffiL rrLauu P''$o".arlo" S
) l'z''"t o! rL'oe'-'^
0
d'a.., BxI Ac, 'y'D+ eL
3.^ dA6x
-Lo. go'
= Bx
*t' '1
t. 'og"
'r€ FY!1e.,'h.{
g
to+h Iq!,
<"-- .b
6C.
D
5'4 <I] =
BY=
5)" / gvo
i." ?F,4
'i le,"Ahl o! fo".,.o
he,"gt'f of l'ttt
Ax. A
B* =) _: -_ B* + Bx -_ Bu",r
^B
' )- loo
B) ._ XY = 5o- tg.n -- ..D4,.
.,(,?-' 4s" = BY
eP
t - 40_ t gD = 4oJ-2.n.
,t> -E;
nl $L' e aJ oa s+,,"^4
"l Lqt - 4<tb ,.
"l (l/(
.A2,
CD
5o "o

l-,,.o .
tor*ogle o[ abvoFP6n oI ob litr +""n f.oi of
1o",,.'
-A^q l" o L
(U
P - ao"'
,b -lr,F. of toe"." &,^" *-.t 4
'{o {e'--a+,"o., &
e {.
"
<,t f''or
,fFe aLova
1k.". ^a
I
I
?i-
I
I lo-l,n
oer.ere^,teJ ,". fu,_ ,J-
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f'o- +,"A,
5- a +ec_
*o.3o"= og,p, -
aaj
.!= ss * B13 Bc
9. a ecp
-L* 6o' ..
itg =
-harirr "b
{a
w
c = s-oJt.
!Pg'= qlz =etat Bc E{"l3.
9r =;
SD.l3
-+lr'tr
CrJ = 5ox3= iSO.,
E , !-o"r.
t{ts Sr t" toat- -a a^d g. & boaf, 1 .
l^'"f6u.r
+ -L,!qr.'t -l-our c =rh,.o = _€.
D fll-o.'ce tu ft.r."., 8,6.. = l0oo.
4aV1e + alr vcr Fr"* rb * {-o- B, ar : Joo.
-A-1le $ el,+vatfic.,
"i A &"- q, F=+d
alave ,o.l
4"-..".,of-"* er
'!re {o".- "b *Je*
,thr
fo
,u€
' e t^
1o" so' -
grB -
?- A +aq
o"@
a +eef
ADP. -
o{
"&
aa./"3 . !, 13 --- O
*o,-,{9o
= 49 + ll
Bq
qS f BB{ : +1G rL
-"F...r." kJ
o,t Ll,ow.,
= 8e
-,4
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:) B,B" = "511'. *',
d= GrB, _ too
€l- t Ji't t
x G-t
€r
= loo({3-r) -_ sot.r3 -r)
L
.l' e ,oql" l- o{ J
'%l-
I -hor, tp = E ol G -,) ..,h
-lI
-le,"3i.t 4 l.".?ta.'= -dB= 6om.
Jnefghr ol "[o-."p f,,c,{ f cb = h.o.
,A"2re oh .teg'euPo."
$ fop o[ tcr-^g 3o_rt
aop oh bufra,%X < -_ ioo
-*n2le oh -{e3yelrrod ob totlo- ofi to-6 .1or r
1op oh turldr^? ,p = ai
il"{ a}ow ,t^
{o.,*alp' 6r" ti regr e1a,..,1s.1 ,%
of f '"6u '" a( Jhou:o
d. ctt r .bx I AG , Dx = AL, cD =a^.
i]^ A eox
+orrd = ofr
= B(
"{ bx
|o.' :d = 6o*cr
DX.,
Ao-h
AL
c -- (Ao -h) f: -.'.
-O
' +a.F = 4s > +a. Ao"
AL
_tr t,
'l)
+etz.'
mz {o,-"
Oo
'l3
= 6o
AC
2o.ls.o.
:> AC-
--@
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{""-Ot@
*l efgt,r
q& s,
"4-gl.
'A.3te
"r al orr*r e J
d 9r Fct-"-
of
&hove
$ ' 6 '.'-e
a Agst
I
l6o-r,)G = zoJa
6o-l-, : lo
=2 [ - 4orn .
+efet f o$ la'-p pot F =+a'a'
D& fd,-r" be F,-r,e"., Ia^p gorFl L*rftd,?< Ac--- zo'[i m
> f{42-<<.'ce LeYt^.12a a l-<-"g6i:t D|1 L&ild.""q '<
t&Y Foar-'
= Bx -- 60-+ = 6D- +o = LDd)'
oh .-[r'4xl }'ou--Le, = 'l-r' '-e l-rcs.
ta tu.6 rhi3_r bo opp or?li -rPltr
t. tqY^nat1 156 (]l
ar rt-,oL-co.
=&b
ok I!hF l.oLtre
v-
.-tlg{r+ +'oure :o! Jeg''elrr'o.-' ob
", +.- +"p ob
ole
o[ deg.av r'cn .'f -t, *..,- ts-p o[ .tr,!l.t loL41=
-kr yvolra 16a l-
Eetau', rt Ppr = ht+g51_@ .,',tCot.
fe.a-ta-E
r e1^, r s.a
^1
c.{ '6^ J-}' ( {oi-.Jir-
lo
pfP.
*!-
h
=Aes,E
_(DSrB =
fo.a
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l. a ABs)_
+'a.p = aA => Bg, = h -OB, *"^P
Ao@ 9 Bs{+Bs} = h * l,.,
{a^., .;-,.p
r-- F
68. He ighF
ct4 c2 Le
-An3la D
I
-Aogia "b
' ''s. = h{#-;,1 = tt++=:_@p
to^" 1a- p
Dr"r lo-c c- teiur..' ahipr = L,ffa.e - 6o.L.:u). f tranEf . rncfyzl.
tb4_ tc,^F
o| tou,x
" "46 - fD mt( .
*qx> c-an
tRr' aLowe
{'b*'" o-(
?-.,
^
Aec,
**F
cle p't.rr'"oo o$
dep..errfc.r ol,
be'F.'te en Co-t
,i0
l-1o-rnali cr-)
-llr o rrro .
e, *. o.-, *og o$ 1oc,.,r.r x = Zo"
q -i.-.- +of -b -{oLo.-
F =e6:.
ct ct- .
ft -nf.,"^tul P" fo-.- oh
= oFP.: 4q
.dj gL-
to, eci _ !q
Rt'
Ra- = 5D
!2
l^ AAat J- ,.-"-t Lcln r< :
^t3*,,
l-
Lo. 3o" . _g = )
E.,
c,l . g(.- p( - noG-
Bq = 50€
so
rfe
t e-a ..Jg
S =se1 1{
- so/ .3-{ 1 =L{-t, $.r. -t.
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D,1 ta.ce
P & to.,c e
betc'se<n c,aw ciq_ = log
^13
,vrE:
3
"h
ca-1 +yo.y1 loe,;,"n = SoG.^F.
o!- ca' 1 *,o. {or., uo = qb/J^ .r^k'
6+.
' +h,&hF of torc*"
+tefsht ob yatL
-+€h ob etr.rcrhppo
-Ange o[ e Lcwa Froco
$
Jf, aLs'e datc.
fu -cLot ro
Dtanp AX -L CD
*o= 46- too,t
X A = og'
J^ ALXA.
Yef>r.Le^+eJ
9. aca,.
fa.,,6 = cx
", td^ 3cf = Cx
De'
= be- cxc
*o- p = co *
b6
*o
loo't- c, x
bA
ta,",1r " -- toot a*'=)
Dg.
lootLr = c-)cJ3
cx = 5o (Ji r_r)
o$ t ftr = looJ- EoC.rsr-D
De = roDi-cx .*€
cx {Ji- r) =roo.
L,. = OD .^
-___- x !:<rt
A-t ,.fi, r
J'-,-@ +@
-l","gt"t
.*€ = I oo.n.
Cp =' L,r.o.
o[1 tog o[ -oct *"o^" +rp ofi toc,rc,
q= s6.
F? 'b -ocb {*,:.o toro.. o(; +oc-c,
P=+t"'
{* "b {t"^.
= r so [3 r Ji) yy!-^
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66. 4+e&+
"$ J.!ht '.L,o,re 4 . r5o n,rE.
"le I {,+ I, ta +*o -,L&l a3p'. oac hrD^3 €a.h o+hc''
-/roqe rf depxtur"oo
"b ",
1= 3D"
- 1.(
.rcprere-ha.{
J ,t *". drt -t houol'Gc {o'-., pb
r. n t&9_
ta'.e - ae
t|q
ron 4K"= !!q
Bg"
R! > I (ona
66 ' **
".iil.,*
+1 e.qh I
-,.€e r:k
-Ajle rb
IF4 o,bcn't
1tq *'. at
.C. a Ata
21,{Bc7
-la,. a = 4G
&cr
t&i 30" - tSo
;;
')r : l9oJt nt.
of tou:e.r = AB: 8.6.
"b Flag rr.r$f gc- _ r
[, ,.ys.
clu".ft"o. ub- +"t "b
eLv-rf-.-
$ taa.6
daira S "ep".-iu_.,taJ
6F=
= 5...
"r,tI
.g
1e
11nqle of clcprer.rioo -fr ", F = 4e
D &Fo-.. te Ft',< co -rl"1og
.-[F, oL,q-,e "lata fo
g
I
3' = e! - B-r, = lso tJe -1)
",^tT
D& fo..t., !'eF.o<<n _rU,
ft_r = l.o1.ft-*i )
(ta?(LaIh
tr.ffF-bb
E{*
a( = 6o9
F' 45".
l'}.;
1
!
't'-
e= +e
6
at,
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