RD Sharma Class 10 Solutions Applications of Trigonometry ... · RD Sharma Class 10 Solutions Applications of Trigonometry RD Sharma Class 10 Solutions Applications of Trigonometry

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RD Sharma Class 10 Solutions Applications of Trigonometry www.LearnCBSE.in


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rll\loLt tL.,o.,-,

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foos = opporilT ridg4Jjaccat rr%a,

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+,k8?e"h oh

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,f LLi(

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$e ".

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{,"a- .' " o I tloo TR 0..

r io L.t o.'9{ a .1 l' 'oo ^glE -4et '

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*o."o = opporil' r-ide

'fujo.. €^F {fd..,

11B(.

9H -oItJ., a4e,L , \ WnÂ-'^ TFo"-"o

lc--6-

EL

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loa: lgrrrltg+;:-l5r'

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HL r p6x15.;r-281

H'--. f.loxr(-\rL i+- ,/

H = goxr_E_lJ._ _ r r.1t

o[ kilz fvom 6-o0]"d

louu

,$o.g 4&.Bc

n =*t.fl.ro.



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? 6lve.

ve ih"c_cr[ l-ct 'rr, .&

Dftt-a''ce \etsu:te..

4"g'. o[ n tcvah'o',

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"b

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^.esY.( e î- nlt aLovt Acnta'

d,2-"" 'fq?' fr (". "-r

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Lnqo .t6ar

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= +o[G)

+ot.Ri)+o Lr

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5t"j'l.-o.

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-- +Dx O?A!

-. . 4,: Sr.>t"r-;

't"'n-,!xr o[ iour"-- qo- -Leiql-,r ofi frn.*6n =s-l.:+.n.



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+c?ht- ,t

J-e-F r.r &l{ L!.r€ it ir LnoLen ol poP.fc.

urrt+r-"

,Aef6ht-

6'o"e'' TEah *tl" 'na.le t.d koLe" gr 'r

ft\-oe-d e = 6d.

WL

*.a-u"

tra'

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y ar,.zt {o 6aLe o pof.F c. - 4-, . = ec .

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6fi6d = BcC&

'ld = +,, H .lr.



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Glts-b1 = 1"tEJa- hG = 2h

(:+€)t, = rsQ.

.1.., = tsrE x2*J-3

>_:J^3

a*GI a.rf"-.' t ff i^+ dz ,.,o..,! te."

I n.m"r.t 4.,"$ g.,.r.. "fiotrt,ir olct,=) I = Es2l-g,

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= rEt>J.3_g

}l = tst2r3..3)

{"ei1nt 4 LsoLen poP" f -6"- fr.ror.r,'a

: rs l>r.r -s)"n

'Le'"qu'r o[ .rqz *t"g.t-.61 t,,- 5-. = A+.

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+d" .h eLvoF,t, oi totro $ fl{_j-=""=U.Let +e,6tl- ofi -16-"- te 11 -,r.: uAB- '

t fi LL't ' vc?\ tlc^t .1tr? aLoue do la Pnyq-}4td"* ", <,h-,. rGe^ i, d*- l-.'^.€t( ,/ i , ^ . ,ceb P, cot.%r, -ABc & i4 cl"Jed- U" ,/ fi t"f*li.1,ts:.18. / ,,."'Lt.*"-

4Jfcrc€^h

I 649 =

Hm



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fa" q = Bou

I ta''6o" = 4an oo

-F= 48BC

-fat 3e" - *BC

\rs (3rG=Bc.

fr_t5 -oBC

tte e- -- +'r/ect ;Gt

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9l Fve.'-q

H

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f ohe.vcrbt"o-, (A)

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J.,"".'otl. BcE l'' fl- t z:c'--6'

L e t 4p Po l^'t "l +d"' ' 12qlu

Hm = cD'gL = /' '('t:, '



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I * '---:!un .€& n-"^Âlo s ,1 A&, *d.:Fn"o = o>eoltF ,rPd e-++----

-4al icr ce " FrfJe

JRo

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.tlco occoxJF.l *o Y""Lle*'

Jeogtx rh ,TFe aLaJc{.r c',ftr, :a-gle of e le "a

(p=+*l ir lto+ic).n. = Bb.

t.c.ii

ro,

!



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fTUJE0

*"'a"*J-',"a"dc

5"t-

Yefett4t

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I,e,t +*hF efi- *e'*" Le +r'n - -4G

".6e"t a^€t.

"'tf. & e

f,cr.,6r = opporili] atde,

-,$a-1trc eal c 8de_.

+-fa^([c

.ttsao

fft.a = 4e.E;7 fon 45. - rt

' f,+lD

+ 5ctro 1H:) x,: H *ro -6



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lL.LeF

Jpt-

Lu Sa pa-vacl. sLt1; aF Afghert- pofnF *,c t D L4 Pofb hrf,".l.) aye I Do.r) o.

1vrv.t-

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.[Fio CD: tDo.o.

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cr6te

ef(attr

fl.od+')ar€ f

D&Fa.,t<.

para cf'r-tF

Rc(1ra(f

ffiftc{..dd

porP"ts C = 4S o, f,.J

4Tle ob- el'a-vc-ho-' {-o- f,,,,?,

r o = eo". tF]

Lel- * t? .t6e po,flh _1irrr vrrhtall 1- Joc.,,, ,6-&

pvo.ch.rtr-

l_er ur d....,-dFL:,Ta* *"^d ''A-." a{ Aôr-n r. L'A&h

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-\er *'f*.U.t. roorlu J ef .

Mor r9^.-..- .9..21.6

fl1 {o-",r .6a

L,., f+r-,

e""+ 18,I oori DF->z- <---{

r-t------------ '/*a're = opporiF r?lp Ij --+e_l

/ +4"<rc"4c rflde_.|r__ _____,-__l



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LLOrr"( = ,48c8

ta''4So= l-tI OO+2(,

I Do+r, E- H- ..---O

lf*t,h eb- .tou.,c,

l"r ,+'4 g' t.

*a.,o -tr- 4eDe"

*an6o"

H=-

ta.

€*.

o&o./Er_ = roo tx,(.la-g o. = 1oc,

t = l9o-^ €*l€-t Cr.. = loo( _fri_r)

L

9 :c = toL€tt).,,,_\ v 5 .- /_, ^ - ".tu U.

.rAz+ D

+ )r = Foc!..la)-)I t- = ,36.6.r_D. ri O

H = .I8xr3t.6 = r.ig? xt36.6 = 236.6"r).

_O

fro.,.7 grouJU

fi = 2J6.6 .D.

pavaco'ut {6'tttrt: 136.6"co

-nxto.''s- aefgc,,f o$- 3a'.acAuf

Pftha'ca LeF-ce., poF.t tDhr.e.

ffr*t L jLLr F ot te...rolrtro P.r

h : Ar3 : tsb .n.

ti',o oliz c h (r) Jhc 6rouoJ.



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*.nre of dca-erePo-, f, obir.t n' farnxJ = p= r,so. = z*Ate.

-+-6rz- o[ &g<,crfm ofi oL(ecr- n * [+xllrre]

LX h&' -- at : bD "_ LABTB

faxl\'a'e]lrF A'gr=x gtg..,t

Ai Lpe ,e prur.t ,Il,t o to,,J J-t"!% q|"'0.,". , XF.. ?r- & ar rl,6.,,a

vril:r. z-.g=ao' A'l':' reJtstt-----+{<_--.1

t.n -t \./ac'ts "-Bu +-!a'-dt, 3$ one- + lf-r?.ctu,-dal t^d. & o .e;

'L Ar, -

* fo.ad

O P"@ )

+

ttd = 'lg -nG

tans = AeArg

ta-1s"= r5oot(

Lr t =- rso .-@

= l5o- gDl r x2^,,' ")

= 63 + o")

*re\ = 6=..1 rD.

hgBe'

: lSD

!+ ISO _ rSO€

a+ 5!_l3 . rsovi

'/ :L = lso _. 5913

= lso_ 86.6

ba[r:ee,, otlec hDlrFo,'r .



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*n2V "h

Le t- a)e,

e-Lvat ro,:- of tog

-J*ct-. go,9,t- A., at =

advontpA S.ou2t-,

-ttseo 4g = tso.l.,

o[- ]o..rr.r 4.o.,,3d.

.4 +{, s b.d t5D.o

CDAD

h"F=

t an r,o"

H:

cD,BD

_tl

,l{5 =2 J =

lEo+a,

: r-J J3. '-(l)

l5O + r+ ^ Lr.a" ->,,/-i,

u /g1\ - rsot,rz )

aef6rr

fi,/:

e

h.

{G-r r(zltso x rj3

= l5o.

: 45G = 45xt +22r>9.1-o

of, -+orue- = lz? q.'o.

+"Aln- efi efcva.LJu-, o$ +"p of, ,lo,,.re" {wo.r r,ecr:ol

poi.t g, € = eo..

Lel tt-e.fr;r ef -l-ot _rz, ctr = t-l .D.

Xt u)e- wep-ere.l J1=<, oto,," d..1a

f" {"..- 'h d,A:"" -tq". fc {u,.-.

43A-". dr ,rlo..-r r.:ftr z>=1d. ##;H5r$- ro. 'f€D,r o^€leJ -l..Pa1,le , ooe otr P.dvlee o,fl<,ft e JEe,.,

to-< =

t^r,;lo"

t5o+:{-

f"O.-o



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Dr1to,rc- beFus"n..,

Le l- a',e 36\t rb

b h t orce 6e t-.-.r"..,

"f Lt'e Yeff"'tlenF

t'V*"" , ''[Fe'' frr.or" tl z-t' =Jo"-

g. *iyr"r il"a- L . fF, F. cl

'..1eJoh -e__'Jheo

fc.r < :

fo.-, :o">Df 1-

zo"1- 1 - +lC -D

(, ." (_1, => 2of It€

Lr.,Da- toJ-3 _-E--la%* olguDlrlo,,r" ol

0

of a0z,,a.l-.15 "b

A ,'4,-fot-.rc"

ac creJ

JEZ

do'--d

+"p f toLoe' {-o- pef^y-6d -- zo".

-f.p ,h toco". -J"o_ 3ol_ Fe

F-ao"1+8 = !b.r.co = 't'-qpo8r g {-o.., (oof o}

ctLn"e, da\a, f- uf.

t!tr* o! tlot -yt

$tt

4nA14

of e)+vaffse

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:GD

€p&D

-J^

'l"fa'7|- ,oX "n-

4" &o

faô - rÊD

*aâd ^ -l-r

:--.

:c = | -

/i\./],

. c1

=hG ]-tG-!) = '.o.,tz I= ?9€ 'toxJ3 =

->o =) 4 l*'3r.o.

lo..r1l

*ot:.. 4 = i+S)ro,

toi,:r' -(-.o.' pP.'t O = po.r-16; - 36".,.



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let 4sJn e fg t-,t-

E. J5o bc,fld .%.1

o$ lAo hrrb,?ln

eLc.,.rffo", "$ 1c3

hr"ftdi'-? 4:soo.

eLe-vatf6-' 4 +Df

t,'L?td.ot F= 60:

od cp Lz, .t92

{ lb-. :-h = *B

ofi to.,-:e" -f..- -irp "b-

F_> r tt *--{

BD = bx = t)c' .r, . ,48 = XD = ..1-r : rs'.D.

5ir{ g ,lq-e.

"rfghF -l-.-fa,-61s h Dio "f nt,!.drd;.d a,2!.

*ctn < = CxAX

? 144 3c)" : alic.

o6

AG.-O;c

.t :cG = a+iS.

*ngte o[

Aoalt o].4V

D ir lo.rz 6eti,,:eu. *orue^ x Lcdtd.%? tsb : >L .

l-et he,.tXtrts of lt>t'te* aLove b,n6,pn- L",A.,',3f b)( vzg- <rc,,t d.r)e- aL-.at". J,ztsa- Fn

+'.- oD {h*. rrtsea fr {o.-.-r{ f6*'" nr al.ouro. r'fr.- z-a -6'4 olro d..ano 4y Il bD ) zAKc- :1f .

.ge,e 46DX lt a *ecFc.,111L

of +o,,,"' t*- t"t6-- "6_

A

B

*cr.r A : Cor- E;? -1a,. kf -- o_r 15-

&

T



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0f i5:

? &o-=

+L=rt!:l = -+') 'n

loq-26t alova

bet ttee n 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!1AD

fa"' eo' = :cI

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-,

?"roudr"s Jo' = g'

D fr bq.,ce bett,eeo $ooi o$ -L*e. 1o gof,.r .rhc"e lffor.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 cAABI

-!- = c+.v3B

cA= g

!3

eBltc4: tt r IV3 ..J3

= 8G-

G=

cei =

4gcd

_8-c6t

t6E

:3=8x5GE

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" $\rtogyot- 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 oê- + fre. 'Bchded'

bFt.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 * = ,49AP

*on sd -- tcAP

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) (---{ A4te"<*-----."l

EA -cn

a l"L

+ e-3,)-:9:It'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,rC

Aoec -

TA

EA -C-A

= <. Lco..",,oo t1^qL,J.

= ?d.

od

be_gc_= Bg+ ,

DLB&

=!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+.9t.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_Al](

. >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 r\LdE

* a.' ed =

G=

=)Y

DPl.Laoce

.Ih-e

dq"'r,!6 hr

ce_--ae.

> 8'5

oLov- doto-

or 'iiôwo

a"tlel +".or,^Zl- i$ of .TrJr-, a,"60a &

-l-A A C&rg.

*ao3o'= Le4\ 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,âre,.ctcrdeJ *4" (J e !t|u\?a

Cl.*+o<gD5-z<-**J[

Lar

Lrle.

-le'e

Id-d ^ Agts

|a^'6cf = .1,

-x-

"r. : xJi _O

J--- CDr n

.!, .

fa.p=

*an.:c" :

4qEL'

.h

Jrf +orci+o: +fi _,(\" \')

r+4o= $€)G)

2o JE .o.

loroa- = eoJi .r.,.

l--.It*ê - 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.

Dê "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 __

II 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

2.5.l"r +,cQht of rûtu,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?"rtnbJar ,<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=eI,

+ cL-tg =:{- =O

) o, # * J::,1 = 4 tJ<ti)\'-<- !" ti- +[J3+r) %- +(a-,E)-.,. A€:ate = +(A+g-

(].cr [tiho-%J u^]ftd.,"â , 4 {Jc , 3) -,bet:,,e'. L<'?w$ff 4(:. r1r.,.

Or"O

Ir efoN"t

D rJ ft\rc 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 "heLc.rat r"c- oF tcJr! rdr

oF ordcrlol l-,e 'J..-lltAFztFr.re = l- b.r.crI

€L

efr

At-ab?- d = eb".

F = ,td"_

th.WJT\-

"ioh

s?.,

aky..,1io'.-

l.

J6,.

datn

l' r-.+*"4?1. crr.

s- ap-cr z-,|-eJ

aJ z-Lrourg.

Lants = ALDc.

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 = aeDE

ta-.3,.,"- -1":Lt)!

).+ 2ll: -l-.li -ri\t:,

>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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.

I

2-8 fl

tove rr 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"tC

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.;73f. 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" - +gEL

Bc -- .+5 . -O/a\ C) /-\C' '" (rj xt +5 = +5.43

{ = isLJ:_\)

- lr r( f-oicc te F14a.. th."-aI

)C .')

- +5t.4..\)

38.

+\'

Lqr. r

_a^

oi

fcw, go" -

rcB.+5x-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.<

{n3

"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(: cDBD

Tar :d = 45oG

J-= 6o r

rlz rA

=593

of 't.,,'- 4-o-.

tc-'Ed r!"

, 6, , rbLrL 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 : AeBeL

f""4S = ee_BBL

BB,: fe9

JoG t :<o

solG+r)

*an <o

B,e =

ACB,g

-3qB,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. < = ABBX

to- 6d - l'\-

,q€ a

Ag:-.D

CD h€ akU

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 ^ \ Ie 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^ acxDfon 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

il--*-*----,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 ?"tnc., te

L

L

: Lt,".r1.9. "h o&e" = BrBo

= Brstga^

,q, obcva I Xo_*-,ot,'* ,i qYeFe!€^t€J ,1.. {""". ofr {g6*cOd 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

= [email protected]

:€oG

\^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€a0

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.-q\e 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,ê datsa i lrep^ner e.,bed fl -l*.ôf qf ,'g "."e dr al,owo

J; ',"9t

t a',51" **r"."n3r.

Jtrz Frc0utde d ^l?t" '1r----- --- ----It,."rs = erori'l-r- rt;, I

i -+.rl^ca^t rPan, I

fcrocl * 4gA?

*zro,:o' = {tA(

-Ar= r^,J-3. -6){-.- @*@

*Je: -h++

*'.lr-]^ =n{{Jr_r ._ I _> q.

.i , ra.,trl -j vr?,

= +r (e+t; = B.r[d. +rrz

"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

iI

I

II

i

I

I

I

I

I

I

i

I

I

I

-t,.'!r.r

l



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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

JVo r--dlua 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,ê

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-4i4sA,Lce"tlt&^

!i. -+ec.

-l,," "r :-fo ApB.

-Lo-' g = t11--' {azr-a"j €r.

ld-to^ 3(] = -Vj2'7! a-

L't-t(1 ": t€ -o

-tr.4ô

-4+.B. '

=4a' 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 +x\ta, 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 = teB(:

*re t'q h I0

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 = "rBo[ 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.'.'21\e ,i o .[{eo

1!g = lo4.5t:.n2J

flroctoJ : lo"i.5.& "r_

3so" lvr16e 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,_ :

4uBH-

g!BM-

go.J3

8o.fe r go _ Aox a_{3 fg

= iie€ "*tr;.r,3

3q. lerleQxr 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

SoMrB

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 = 48BL

cf -c..1 athglcda be

rcp-rereoled F, (o*^-

:- 32.6.6

e.

r,Av

.1. -iq \ F +*"^..Sle &{ ,,,e_ "fi-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;1D ir Fct.'tce te h-.,e<o F,?alt-oria* FeL = Zok-.r.

'I[, o,Lo,te ron {o,.âh'o., & reg"ercnt-ed

ff tj ".-""' "b -{ i6."c 01 r hog.,.-;

]i -pr +.'atu q w "'b JR.

"?. 8ce ,I[po Xto. a = .,4s

A?.

L&.6o : 4A*"

Ar = 4\Bv-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=

ABAE

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.RD Sharma Class 10 Solutions Applications of Trigonometry

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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" - CrAA

l: aAX

Ax ' ' 41' ".t

*n. 35. = xpAx.

-L = rov3 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,%'.ta)

d fi t a,"ce

t)-RD Sharma Class 10 Solutions Applications of Trigonometry

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+3'1

-i---142iri+

ll+I

lorI

l**l

+2.-t-|e .!rrr1"6la

4'xylc+l-etht

D&hr"c"

+le it3hF

+''llht,r

Jq!

.l.tr\e.,

"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 = xpA,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 oltv lc-.,ela r [$e) = co -.I-

ot t"n-"- "bz CcD = r"r.,,î

$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

Lt ata r( :

'lc,r 3o

LA

AIC,X "

"= tZCx.

= Ax.[i.

Al("tl = ->

cD=

l,J icllt,

4.,%trt-

E(eXB:

of-

ot

48- Ax

t..-pL

i loa

=:-|-o

:6-r-')3

- 5o- Ee3

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 : 4gBD

-tar 6q," : g6Ct

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-- < = ARXF

.la- 4e" =

XP=

3Q. =

Ayeed -

Soooxe

3DOO.,-r)

x q - xr

FA

3". i.,.tel

+o-p = 3qxq

ta^ 3d = 36rp9xq.

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.._

+eRD Sharma Class 10 Solutions Applications of Trigonometry

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4t.I'e r*^gla

4,13te

-4,'oe\a^c l.avatte) -{' Dfi 4 +o g,t

et+valrbpo. ol pogt A =u"at-a va LtL- oh PoP^t R "

4g

t,.h

"i

-6D

FQ.

A$*

"hitAc n

=1- 6,".,rle

-Fo^F = BCxQ

la" sd= t

xqxQ=€L-n

= JE-r= zu3 ,f3

-t"l

lo r

6ox6r>

z\o{-z

= 4B v.,-.

-- Z'fz x bax yY

L^" lt .

4"&t"r €b ae'o3\a.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)- = AP;

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)ê- + F.,cl..Ja4

*a" < = A^Lx.

ta^ 4" = AXCX

Ax = 6-1.

.LLA^F=

*o- 6o'

gD -^LA &cD = g(.

+eBD

=5oBD

5o\.4

Ax = ';n=

-r). : gD.!1

cD: 'q8- Ax ,- Eo- 5pa

= 59te re).?-

5!C&:pJG

+'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.,

t\J' 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- rltTI 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 -.-',. tcDl1"; {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,,r sve r,o^ {o -.-abfoo & t"p"e'e -teA B

Ctl {houoo.

t =,!c.r +-,}.,Ut. 16 o^. $ Jkr.Xc(uded a,t 14 $e Grv

LnÔ : cPPol' Lc lt.le,

"A{io c-e-Fr ide-'

.'t\ort C* I Ag, Cx _ BD = 6D-n.

x.B = cD = AB_aX,

to^ ". = _AxC^

I-ra^ 4s"= AX :> A(:6D.q.Lh

Kg -- CD = SB-R{: go -to:: Lo rn

fu;- 4:".s r,..

{*- oh t,3q

I.. IatI

I

J=. ".!,lrar 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-xAx

atb a .A\ colBr *e)

F-+t#

qiAXx+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-<, taêl;_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! tFHo 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.\

^YAe = .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= bnG

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-rI

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 +",hÂt.

on5t'. &e ntr*

fan rso = Aq

^Y

Pq

crloo'.,.

cloc' J

!\c.Ao,,-,

3".13\L

-Ga -tcr k cx=t59ty€t kc A)e

r.; ,_.nt^.

c.1te-

:) u26g= +,

"Y-)aLr-t,l_-r)

i--.,ee

#,Â 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"'" -

iII

i

:I!

i

I

I

II

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 t6nclo.,,-.-, xA -LPg, , Ae =,r,..,,D'il o^.. dl) rrottJ {'*v

rs xQ,

ta^ x =

O -o :-z Lu-^F- to.,n = 21,

l! A," qCas c( =

dqFa & vcgrcr <-^,tzd ,: 4.-* + d Jgu"c

5o 1d1q r

.LL.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,ôtt$.-.

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 = roaY

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="4I 4,o- c =F.

"'.fY cr€.-\t ed I {,r-*., o}-

P

QX.

+B

4eQx.

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- ,4xQx.

916"13 . *R -a ^| _ -{rlQa.

e=rID 'aF

a=AB

-l'e,it"r ob

DIr Fo.rcn t{*

l-A4e

.trola -hâ- ----- ---- 1tr. < .

e>r:49 =ta"xo

ta. x *14^p

po." = o**ltF.,.^r_r"û;

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 = atetL

de

'd

_lJt"^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{_ = a3,?'a -Irbn p t

AP-Ae'

=gAB

o*o@-o

/=\-e,-@

@.Re-/

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^ -AgBxlana . 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,- riaeA$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 fgttlan ,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(

!5BU

rf.3. -n.

I xq LCA, zktJU

SL". b3 = ZtALV

cz : 'J--./:,

\

cz -- L.6q'+ .r,.

ol'u

J:=t

ar.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-iUFo' bX.-h*hF 'b L-?(ct'-?

/ ta't6oa 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' '1t. '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" = BYeP

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 of1o",,.'

-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.". â

II

?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

{aw

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=+dalave ,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 + llBq

qS f BB{ : +1G rL

-"F...r." kJo,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 r1op 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-hAL

c -- (Ao -h) f: -.'. -O

' +a.F = 4s > +a. Ao"AL

_tr t, 'l)

+etz.'

mz {o,-"

Oo

'l3

= 6oAC

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.

=&bok I!h\F l.oLtrev-.-tlg{r+ +'oure :o! Jeg''elrr'o.-' ob ", +.- +"p ob

oleo[ 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++=:_@pto^" 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

,i0l-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 _ !qRt'

Ra- = 5D!2

l^ AAat J- ,.-"-t Lcln r< : ^t3*,,

l-Lo. 3o" . _\g = )E.,c,l . g(.- p( - noG-

Bq = 50€

sorfe

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

-Ang\e o[ e Lcwa Froco $

Jf, aLs'e datc.

fu -cLot ro

Dtanp AX -L CD

*o= 46- too,tX A = og'

J^ ALXA.

Yef>r.Le^+eJ

9. aca,.

fa.,,6 = cx

", td^ 3cf = CxDe'

= be- cxc*o- p = co *

b6

*oloo't- c, x

bAta,",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''

-/roq\e rf depxtur"oo "b ",

1= 3D"

- 1.(

.rcprere-ha.{

J ,t *". drt -t houol'Gc {o'-., pb

r. n t&9_

ta'.e - aet|q

ron 4K"= !!qBg"

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.6daira S

"ep".-iu_.,taJ

6F=

= 5...

"r,tI

.g1e

11nqle of clcprer.rioo -fr ", F = 4eD &Fo-.. te Ft',< co -rl"1og

.-[F, oL,q-,e "lata fo

g I 3' = e! - B-r, = lso tJe -1)

",^tTD& fo..t., !'eF.o<<n _rU, ft_r = l\.o1.ft-*i )

(ta?(LaIh

tr.ffF-bbE{*

a( = 6o9

F' 45".

l'}.;1

!

't'-

e= +e

6

at,RD Sharma Class 10 Solutions Applications of Trigonometry

www.LearnCBSE.in


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5. a'151 ,

.|,e,!t r

61 . +l ea'flht

kF 7oP^b

p",0. t o

3'"*+" "i, F

] 01ur? ed tu

Ifu aLpv"

O-l (hocoo.

C. aAsL)

f^ a 4e,

...arffpty- O*@

tana - ,{c.Ap

tarr 6d= &"e. =AI)

Ltg

"h

q-

r": = trgrh r-r. 9.& "+ h = scJ-ett = 9,r p.1g > = 3.LrMh -

-t Ia3r|" bh :3.6-cMt.

pYov. *{'ar h = 6..,.h .

daha. & v1'ertntz.l ,l- 6o {e'"- "}- (,b""

la^x= ABk.

la^"r = b1

b"p= 4s = h t ,3'n.--leD1

*"^ (qo- /) = l,3

o\ loacr ,+B = 'd'.,.tt.c LL 4-k $.o"" B , -,{.gte + e tevatrL i' <

Lr I '.h $o.o. B, -&o2ra "i et".rot3o. t p.a'r? to'n7le-'.,l..-t4 . ,(+F - ?o" :> F = 1b"-d.

h= qthtc_@l^,<h= 1fc.^,c x g coFa

= 36 .Ctao<. cof*)hz = 3sn= '/:6 = 6-6.

4 tou:."r = 4.."|;'.



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.68- +tr-t!1t.'r

l-el q* q

4..'la ol0l/-4.nle r[

.i.'....hf aLoe

oL.thqr4,g 4 Aa{

-:L^

"b l,frlf, Lo-.r" ,+s ='1,'."rrt;,,.te ohfu d&to,-re te l.,:ea., {hft{ !,1_deg".,<,%r, "l {, &. sr! ? zer,,^.

c{eg"csr$" oi r_, 16 = +{.dat-o ft r3'ae"lzd f^ {o* ob e.,-"

*o",e = ABI _:-

r{Luan 15o = h

Bsr-

--.=h-_{DA 433, *or, < - l\8

g!rtz1^ Scf = 4

AgL

= 2 oo [Jg+,; '=

Rs+ = h(i .._-@

Bs, -es_. = ;,6;i_,aoo = h(e_r_)

|r = 20." ,l \j 3-t Ifci Giih = too (t..r31 ,,; . 2 i j.2 Mh.

+e.fgut- Dt- .tfgt l L'o.ue = ,t3, dk.

t oo (J"s r ,J .ra L



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RD Sharma Class 10 Solutions Applications of Trigonometry ... · RD Sharma Class 10 Solutions Applications of Trigonometry RD Sharma Class 10 Solutions Applications of Trigonometry