ࡱ> y|  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwx{Root Entry F0NC}"zWorkbookSummaryInformation(DocumentSummaryInformation8 \pUser Ba==hi !~'8X@"1Arial1Arial1Arial1Arial1Arial1Arial1@Arial1@Arial1Arial1Arial1Arial1Arial1Arial1 Arial1Arial1Arial1Arial1Arial1Arial1Arial1@Arial1 Arial1Arial1h8rCambria1,8rCalibri18rCalibri18rCalibri1rCalibri1rCalibri1<rCalibri1>rCalibri1?rCalibri14rCalibri14rCalibri1 rCalibri1 rCalibri1rCalibri1rCalibri1 rCalibri1rCalibri"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_) 0.000 0.000000 0.00000 0.00000.0                (  (  (  (  (  (  (  (  (  (  (  (  '  '  '  '  '  '  '  '  '  '  '  '    !   # ff + ) , * %    P  P       " `           & a> $            H  @  @   H,  @,   h@@ )   h @ )   h @    h@@    l @    h   h,   H  H   l  `      l @    l @ )   h@@    l @    h@@ )   l @ )   H,   H,  @  H   H   h@@ 9   l @ 9   H9   h   l @    h@ )   h @   h )   h@@   h@ )   h"@@ )   h " @ )  @  H  !x  h !x  h  H !x  h"@ ,  `   !X #X  !X  h #x   H   h #x   H9   l  d  h   h@@   h@  `@@ ,    H  `@   h  @   h@@ )   l  @    l  @ )   h!@@ )   h! @ )   h!@@    l ! @       h@@)   h @)   h@@)   l  @)   h@ )   l  )   h@ ,   h @ ,  L  H   h,   l   H   h@@   h@  h@   h"@@    h"@   h"@   h@)  `  @9  `"@   h " @    h@@   h @   h@@   l @   h"@@   h " @   h@   h@   h   h @   h@@    l @    h " @    h@@   h"@@  ||%}A} 00\);_(*ef;_(@_) }A} 00\);_(*ef;_(@_) }A} 00\);_(*ef;_(@_) }A} 00\);_(*ef;_(@_) }A} 00\);_(*ef;_(@_) }A} 00\);_(*ef ;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L ;_(@_) }A} 00\);_(*23;_(@_) }A} 00\);_(*23;_(@_) }A} 00\);_(*23;_(@_) }A} 00\);_(*23;_(@_) }A}  00\);_(*23;_(@_) }A}! 00\);_(*23 ;_(@_) }A}" 00\);_(*;_(@_) }A}# 00\);_(*;_(@_) }A}$ 00\);_(*;_(@_) }A}% 00\);_(*;_(@_) }A}& 00\);_(*;_(@_) }A}' 00\);_(* ;_(@_) }A}( 00\);_(*;_(@_) }}) }00\);_(*;_(@_)    }}* 00\);_(*;_(@_) ??? ??? ??? ???}-}/ 00\);_(*}A}0 a00\);_(*;_(@_) }A}1 00\);_(*;_(@_) }A}2 00\);_(*?;_(@_) }A}3 00\);_(*23;_(@_) }-}4 00\);_(*}}5 ??v00\);_(*̙;_(@_)    }A}6 }00\);_(*;_(@_) }A}7 e00\);_(*;_(@_) }x}800\);_(*;_(  }}9 ???00\);_(*;_(??? ???  ??? ???}-}; 00\);_(*}U}< 00\);_(*;_( }-}= 00\);_(*}(}00\);_(*}(}00\);_(*}(}00\);_(*}(}00\);_(*}(}00\);_(*}(}00\);_(* 20% - Accent1M 20% - Accent1 ef % 20% - Accent2M" 20% - Accent2 ef % 20% - Accent3M& 20% - Accent3 ef % 20% - Accent4M* 20% - Accent4 ef % 20% - Accent5M. 20% - Accent5 ef % 20% - Accent6M2 20% - Accent6  ef % 40% - Accent1M 40% - Accent1 L % 40% - Accent2M# 40% - Accent2 L湸 % 40% - Accent3M' 40% - Accent3 L % 40% - Accent4M+ 40% - Accent4 L % 40% - Accent5M/ 40% - Accent5 L % 40% - Accent6M3 40% - Accent6  Lմ % 60% - Accent1M 60% - Accent1 23 % 60% - Accent2M$ 60% - Accent2 23ٗ % 60% - Accent3M( 60% - Accent3 23֚ % 60% - Accent4M, 60% - Accent4 23 % 60% - Accent5M0 60% - Accent5 23 %! 60% - Accent6M4 60% - Accent6  23 % "Accent1AAccent1 O % #Accent2A!Accent2 PM % $Accent3A%Accent3 Y % %Accent4A)Accent4 d % &Accent5A-Accent5 K % 'Accent6A1Accent6  F %(Bad9Bad  %) Calculation Calculation  }% * Check Cell Check Cell  %????????? ???+ Comma,( Comma [0]-&Currency.. Currency [0]/Explanatory TextG5Explanatory Text % 0Good;Good  a%1 Heading 1G Heading 1 I}%O2 Heading 2G Heading 2 I}%?3 Heading 3G Heading 3 I}%234 Heading 49 Heading 4 I}% 5InputuInput ̙ ??v% 6 Linked CellK Linked Cell }% 7NeutralANeutral  e%"Normal 8Noteb Note   9OutputwOutput  ???%????????? ???:$Percent ;Title1Title I}% <TotalMTotal %OO= Warning Text? Warning Text %XTableStyleMedium9PivotStyleLight16` tintro:solve triangleg \N   MbFy՟Nu]&"ny՟Nu]&PNG  IHDRÜ6jbKGD݊ cmPPJCmp0712OmIDATHOk@<ބxBs" ,vn<؃oPK{rEČN2LO2e2?Οż8Y󆳇4)5,o&+ecvL/V"A126]EySstdNf@J9Z}OG/:YPzh>PѬ9h -W.u`uON8.WтSů C0uJP,vޥh_ źM ]gj`ټ.橊ӡV75>>6 ܩcR~8 G;,~L}_ 8 #惥A].r{šQ͠'P'  Ø%bVi_T9 7 E t'M w"wH_v7NXy$N Pa\&|½ni\^UhMsLEvz)JؘdEqhwqIOa{}|3)b~u*gIFxMathType001 asin(A)=bsin(B)=csin(C)a=bsin(A)sin(B)A=sin -1 (asin(B)b)iWIENDB`b^my̹g{,z:n2my̹g{,zPNG  IHDREpbKGD݊ cmPPJCmp0712OmIDAT8ӿO1pwGܟJELUGƎ +b`B?RTUCf*`MQIhb%[-YGhF7^ !\q]ȩކZdR?BowTPK9sNf6mfӸ6g'< TK˂w e1 vj_훞קgD|ja]1 zѫלmI)JlW|CR؍K!xnY?qB mq7Oֹv~DqWQg=F#!k+C% \Z,)v@;Tb=#6b-॒ '7⟪0k4%=NU%'=VY{1Q 8;-;BIFqe+̊3f3b)EMEJ? U6{)%]'*^>/NIxgIFxMathType001 c 2 =a 2 +b 2 -2abcos(C)C=cos -1 (a 2 +b 2 -c 2 2ab),IENDB`bGQ7 vNcs$ B"#nQ7 vNcs$ B"PNG  IHDR*j#n!ZbKGD݊ cmPPJCmp0712OmIDATX1lE/:$8,9xKJU:(h-((Ŏ\:\I(HW@;;x6yݝ}D DX7ous X+̴Zz{5}U(e˄nz5n`zFMlF†hsy1J}XƎʦPYo-FBNw1[>{#Gb6xJZ&D͛܉mM;/bӝ(%{rp8 DgRe8oʽ]{;މ2: ݓ,?:O>̛_J .b,o䵵0M¸n(+m6 BCQ3z0e3b͑j^}vyXr̬O `\4L,F˵ǸijpOUCGjCĔх7!}lAɱ{jץ>ׂSm ]WB3920dW k,Ȓ`UEkҲ |BblCgIFxMathType001 sin(A)=ac  cos(A)=bc  tan(A)=abA=sin -1 (ac)    A=cos -1 (bc)    A=tan -1 (ab)a=csin(A)     b=ccos(A)  a=btan(A)  tIENDB`b?+$??P4]Pn+$??P4]PPNG  IHDRjh1X1bKGD݊ cmPPJCmp0712OmIDAT8ԿNP& }#&0#02Sdߐ9-w2(qR˹wnpT_q:#GIhDaq"Reڔ w(L-FM!!`Wzk>sTW;0'0+WH&4oQ˴d4B~ֈ9u@0WM×d3u*F?J%nnʴwW#>PNG  IHDRj3PLTEU+U+++++UUUUUUUUՀUժUUUUUUUUU+UU+U+U+U+U+UUUUUUUUUUUUUUUUUUUՀUUUUUUUժUUUUUUUUUUUUUUUUU+U+++++UUUUUUUUՀUժՀUՀՀՀՀՀUU+U+++++UUUUUUUUՀUժժUժժժժժUUՀժ+U+Հ+ժ+++UUUՀUժUUUUՀժՀUՀժժUՀժUՀժU+U+++++UUUUUUUUՀUժUU???kkkubKGDH cmPPJCmp0712HsoIDATx^kܨ.q6 ! $թ3NO/M?VZtiXk'ٿ+#{ӌ3wcwDI"${T7x3jKCof!x%Fm}m~PX@ 8o.W'(ڿzy3(,5m*OݼBlwQPUt6  QvBA`>6 CT|0(Ջ((,K-(~Px!TZ7ޭe'@v+!B_}J)X$NdAxC>["'ŐdJ3D˹O;QQ5a%?KY_9,K0ji񅛳c@8$'x +`ЛC! c$@+A?=>G`2@xbKN43B{.Z .D,R˲!DA|!;:T hn0;nl (]]D q`D7 hY 0|o)V-dp\ahtW! #t ͎,@>26'7c!)mZd_ ֌@W~Bvk"Ȧ>GYl=*4l-?H?4RUhB.{˜/K8@%C'5AXgzKuG0O>=CNF5*iIZtȉ3{{G5r1ڊ trra~@AtI"V##%{ b3md1؍FPuZqt~o-H9^#"jojfX=@7,cĔ$*S]}>4y 4G0Fb֌|WяEJJ/%>(78_!VbǍ=}Rn?8*P;ˠB .[3nCRXT7Z\EPcʜ'z7ӚFi f+d9='/}`= 6ݫט)(Jm6 !"XbӋ; !nGg=I&?g`.2D3D@axzr|,tTrFNݣ0U#@Rw,R14mn1 Ij 5v҄"c>ZظKtE<=@}'VKc-6)~pŦ9VKAC.176:Jܽ2*#?*P)Y,k̠s f?eH66蝡hWp.pzWi~Џd 6jAzB(aTA=~evky]C] ϗɠGq c ,cP7rupC,JEwD#@{~L xn&O*zиG1#P *{vc_ +[;tWM~Sg+eϤė,վCSB'12UmAl 6*/t{5S3jAd40 bQ6vl*Y建8)/rOЃ͖D\IO9|S-t8ڞd_*N _|`.:rԡbO=Je4x&JU6[$_.UH'ֳ@,i+\7!P\h 5O˷l@[N| hEʞ}$eUÐ˘nPk~phDNK?y(R+0%lI'Si.vQ"HJy 0;=R" ]p18P2] N_zގazSyYJ=(9/@!g-ۣ-]h%T $'=ҁ+4E{ P}KaZ-~K)ً߉n[ x*F„T1n X aM3^V 93۳\(רSrqe9 ,fʹdT+DBnrlQyu> 3&rP )_`iQt<~a3ҴW䘶=d`)KI>]S.6F^&8nd?S¤Uf1t ]u*83x!# vCX a= ȹ.ny N(W|P)&?TGvcbvfg,`T j(xG 5 `5DC}?ߒ]hΧǑx>ٙiVY173'.8GZ =U "mg xׯ\\mOt"@+ujE^q=,qcSJc> {oa\ 5 *I{Bm$i΀&Fw^&eР2~nccu#8a`~0 u7ܟɋPz/ ( EeA'[/H oy€.+/&XS28i_<\_<`C'^ $-mZ0,sL>KIvw[Ow^W\ٙ~.yjne8#$ ; ny] q?_:{†&)6jvw<`+4+Ӝ(L㌗Zvnv֌Ldxx9eّ"XJ4c \`Tǃ1T1+gm|Z1LζbaC#evYn-smP 6g{c0s],KG E1ЯXF[FK{[6O1(j ?ZI; nzccG1lkA⦖Sq=kr'|;2d+M~ |P0œ.M ^(!;VN"L =K/xXIs{.y Qy|PAc鼹8b(Y;jZУlpr"?φrV.X=. .$=-MaGh2=~ə䫻d'P( sd0Q`e #Q 6!T$:v2rfbaP,X 7TUET8W 2`^û b( HLl<=œMjF* .p]DUf5>cto~;&2eF/҄P{saC:ym[$PqD; C}qC50ѻq.%$Ju6A5EM0$H]|"NG dXB FQ8+qcb ` ^۬ɐ<,/Q_"!K{a֘TCin%rs,k~UJ>cR.Lt-vNDmM(D$ͺ2KcAj>_. 0gJJ4J2  Bҩ[`}zqߴ]gxۉT OVY-׷ݱOe:L|[ u)BXGeH_]2=1vP/3Yo姫oܳC=1MOmT3S:c% (a#۳˞L TXn j̄r_|zۣg:2(40跎Dp^[5ϦkLS[s-M>r;g08T5%hH3+&4Ħάg"pF>>E)x>ʻ ˑ>R(-h1HA '`k>Oc9,u0(%DsR:ŢZ@TAzWKƺ4n>طq( :񒎦IA e%).I4b1 f˗ɯg e!4|cn_:ÊxEuf$\tfY&Jg/f#qgE. +X ۝Co#'3Ż9O2ώaw'+Xb ߁X8 &̱` G»љH[7n`l$r  Ieѐ# 6lX+6kĻA( 6j̻!6iƻ 6hλ#"؞g`Ov}M5ïx2g""ؒ& <6v 7nH 6cmHqk`#y'&o-74{kv.^EmW޽\ @6!X0WxT3 UBk*C `@^5`P t"b1iE*B#X|`^:08H |`ؚl`t m"iނɟqxy9 f$ff `a/R$Ѱs'<>18W!Z L%S5|g#j8<\y~S[8Ί{ʎ)tڈ~Gv+u;p:zJw/4&o>^T ׀;gFibZrخ+n2Q8%wҷW~Tpx؅śh>*?\![w6 Kֻ ̡jwvFjX)t?p0 tg-94K;s<.Ryz5\UEd6yCî{KM8\`W&Ϲٞa/šIENDB`b\lg^Ðܮ[{8n0lg^Ðܮ[{PNG  IHDR :PLTEl nޚޛߛߜߜߝߝߞ࠰ࡱᢲᣲᣳᤳ⤴⥴⥵⦵⧶㨶㨷㩷㩸㪸䪹䫹䫺䬺䭻䭻宼寽尽尾汾汿沿"UbKGDH cmPPJCmp0712HsIDATx^[ Fgs-(Z<:?* ,E,Fp .=)#| _—K/,d-ӉO2@.잸4eKˑ6}0_C⨁1T #I%;#z7G0Q9Q"~3a5zȕ$ѻ^W{yι8Kң0$.gq:I`zyz%qY m\ޢ,\)撰Se!A.)3G[+dQǥ#eĹ8a\*xQFeP\ntqʀtgB]#q Y/BRŗ.4eK2w\{t5o2\Wy5\:/l(s]A=\$Z(3.\4|s)̲ \0La!L%)s LJU.[Kͭ>^KS\%zlؗwK'#V)5wLiR'j_exb4q^H\%%PJ~jLK䵯=J((臒]=w|%!-;_>٢2ekCr"Dʿa:R:7i%ⰔN?F(^H١ A=0^[I20pfY(n]eI!}>&J+kb&j(C2$ eZ^FM/P)(KPr–E<Ȯ)ࡠ{uʪtUIhYd};zRv#H-{Ovބ0kR*@@grp'1)QJaRr5%1 J RLcW(@iȁܹxL)yM/ܞAB!Bׂ-)Kl$Zk*(mK)+#MkFdCUA;`s3l%eq%y+rDʠ%AɃl!QkjuʔxdBZ>kNMc~{rP?_"!KJ,^=YDZz6)ɇ,Ĥ_C)2*Wjˆ]ˀ`06woLH?Ե0%3bvj=2)]x>9%QR$VJaߣ,%X;Cn!.Iw<3!>-gJ9xޅ3޷srt9Ѥ{<ɳƿA^;엳z^Az^A^if1}U\tnI3')Zv[w(x??7ڣW엿$f/,K )P=y^oR.u+ZV/;̡ T]p"Ҧ7hP$J&c_O4X)#(',T+wP kLn*j-U }& >_i9Xe9)w\qܳbU=%W1|-mJ<|Jxk8{e:Mo2׃*V+BNRf;5{ME<6ia =c/OSJ/T^- 8ZyhWqu~p"m~ROoI: ;6IENDB`b"Fn?n"Fn?PNG  IHDRb|PLTEU+U+++++UUUUUUUUՀUժUUUUUUUUU+UU+U+U+U+U+UUUUUUUUUUUUUUUUUUUՀUUUUUUUժUUUUUUUUUUUUUUUUU+U+++++UUUUUUUUՀUժՀUՀՀՀՀՀUU+U+++++UUUUUUUUՀUժժUժժժժժUUՀժ+U+Հ+ժ+++UUUՀUժUUUUՀժՀUՀժժUՀժUՀժU+U+++++UUUUUUUUՀUժUU???kkkubKGDH cmPPJCmp0712HsBIDATx^[*,D"PwpÙ95~Ph.ޏy#y/J,W*+X̴ySyч # (vH|IXac(9,(e 2Kķ)-Jt BĶ(-DJd Bĵ)a- JT ¢Ĵ (LJ\I>ƧE@fPYDw+H-=`"lj۷vGE@-(\t%T~?v)"l-(;mі:؞7߶cFɓ :Sq N[A-xs*\P.>B!5 eS>LjZfaޯdGdr->^`öSIue[*|$sJ.^XK|q-[7 RRe,\}/SdΠ,m ;ƅ>%H1փԑJKDc!KtEW&`޷ >n.-(]dֳ4FPbJڲTbGiz(b!e"¹Ttx鄂/+--)%!PjD_.rI.Jq  Q(wK jr4.oeA9W!e <"ks "Nz`JRrнd4 ,u11g<`QsG1 X[FR-C)S`e42bgO18P,# C18Q,,=]PٍEHѶxR-]/ELѴxS-=?Ee@QXbPT,A((K"H-(BK("H,(K8 ¶p-)LKH ²p,JAdBb?/a)\R KOD'6!_,(Hp? 0߾)lMn,w*0\)0xK$J}qŗZkq AZ)ap(0(+eKپy /A(0\) (}Te.J2%Y_rX*b:J0)Gş3z| ] JI?{o {Ŀjܖ+qm m w~xP8IsW|UƆhx*Ȥ4ٜJ})Sɵ 8OϠ <**DW*Vjn=|A-}~u0VZhu0Q &jU`91_fÙR1m^W*̆3mbڼ̃T gJŴy_0tKIENDB`3 A@@   0^Solve a right triangle.Solve any triangle.Use the Law of Cosines.A isB isC isa isb isc isInput leg a and leg b.Input hypotenuse c and leg a.6Use Pythagorean Theorem and arithmetic and basic trig.A is =ArcSIN(a/c)*180/PI()c is =SQRT(a^2+b^2)Input angle A and side a. B is =90-AC is =90b is =SQRT(c^2-a^2)Input angle A , side a, side b.ba C is =180-A-BInput angles A , B, side a.C is 90.A is =ArcSIN(a/c)B is =ArcSIN(b/c)c is =arcsin(c*SIN(A)/a) =  < no solutionbsin(A) 1 solution 2 solutions >7 Input sides a, b, c.Input angle A , sides b,c.b is a*sin(B)/sin(a)'c is =a*SIN(C*PI()/180)/SIN(A*PI()/180)0B is =ArcSIN(G37*SIN(I36*PI()/180)/G36)*180/PI()b2 isc2 isB2 isC2 is C is 180-A-Bb2=b1%c2=a*SIN(C2*PI()/180)/SIN(A*PI()/180)B2=180-Bb is =a/TAN(A*PI()/180)% solvtrg.xls`Cells for the easiest triangles are at the top and more complicated triangles toward the bottom.8Info is computed in light blue cells and in green cells. INPUT info ONLY in YELLOW cells.NNotes and formulas are found in darker blue cells, white cells, and red cells.Solve triangles. 2007, 2008, A. AzzolinoSThis spreadsheet contains cells to complete the computations to solve any triangle.% Solve a 45-45-90 triangle.% Solve a right triangle.% Solve a 30-60-90 triangle.8% Use Pythagorean Theorem and arithmetic and basic trig.% Solve any triangle.*% If not given a side and opposite angle.%% If given a side and opposite angle.% Use the Sine Law,% Use the Law of Cosines,Use the Sine Law,+if a side and the opposite angle are given.C is a=b, a=c/"2, c=a"2%Often these may be computed mentally.a=c/2, a=b/"(3)b=a"(3), b=c"(3)/2c=2a, c=2b/"(3) Input leg a. Input leg b.Input leg a or side c. Input side c.if #NUM! there is no solution.-Seek no solution, 1 solution, or 2 solutions.Seek each angle.Seek the hypotenuse.Seek a leg and the angles.#Seek the hypotenuse and the angles.!Seek a leg, side, and hypotenuse.Seek two sides and an angle.Seek two angles and a side.Seek a leg and hypotenuse.Seek two legs.-C is =arccos((a^2+b^2-c^2)/2*a*b))*(180/pi())-B is =arccos((a^2+c^2-b^2)/2*a*c))*(180/pi())-A is =arccos((b^2+c^2-a^2)/2*b*c))*(180/pi())&a is =sqrt(b^2+c^2-2bccos(A*pi()/180))b (yNF;T OϏ ͐ ccB  B̖t  dMbP?_*+%&?'?(?)?M6HP DeskJet 830C/832CXC od,,LetterDINU"4$2 $$$$"d,,??&U} mj} m} } } $ } } } }  B @ w t wt ththtt ht hp ;j ;j hphphphphphphphththt;;;;;,p,p,p k2 jj k7jljjj l8 jjjjjjj(ksssslsssssssjjjj mmm 5 mmmmommpjqmm 4 mmmpqqmmm 6 rpq*qmmmmmnmmmmmmsmmpq qm {9$mmmnmmmmmmsmmpq qm {3$mmmnmmmmmmsmmpq*qmmmmmnmmmmmmmpppq qp v1 z" pppppppppppppq qvv z: jjjj jq wu v1 {K zX pp vu v1 {N zY ppp qvu z< jjjjj q qvu v1 {K jj  zX jjjjq qv v1 {L  zX jjjjjjq v1 {N jj  zR jjjjq qv v1 z yxjjjjjjqqu v1 z yx  zT jjjjq qvu v1 z zj  zS jjjjqq|pu v1 zpyxp  zU pjjjppq q| v1 z"ppmmmpjmmspppq qmv v1 zC ps zDspmmmspppq snn v1 zsssp  {V jjjjjjj snn v1 zjjjj  zW sssjjjj sl v1 z psvssssssjjjj sss v1 z#jjjs  zQ jjjjjjj jss v1 z$ssss  {P jjjjjjj(jjjjjjjjjjjjjjjjjDp ld,BDD.DD.P@FH<dN^NhlfPfddNdd !"#$%&'()*+,-./01256;7;8;9;:;;;<;=;>,?,( jjjjjjjjjjjjjjjjj(!jjjjjjjjjjjjjjjjj("jjjjjjjjjjjjjjjjj(#jjjjjjjjjjjjjjjjj($jjjjjjjjjjjjjjjjj(%jjjjjjjjjjjjjjjjj(&jjjjjjjjjjjjjjjjj('jjjjjjjjjjjjjjjjj((jjjjjjjjjjjjjjjjj()jjjjjjjjjjjjjjjjj(*jjjjjjjjjjjjjjjjj(+jjjjjjjjjjjjjjjjj(,jjjjjjjjjjjjjjjjj(-jjjjjjjjjjjjjjjjj(.jjjjjjjjjjjjjjjjj(/jjjjjjjjjjjjjjjjj(0jjjjjjjjjjjjjjjjj(1jjjjjjjjjjjjjjjjj(2jjjjjjjjjjjjjjjjj5QQQQ6LQQL7LLL~8LLL~9LLL:LQQQ;LQQQ;aQQQQ <LQQQ<aQQQQ =LQQQ=aQQQQ >QQQQ>aQQQQ ?aQQQQ @D,,,,,,,,,,,,,,,,,,,&&&&@ ;A ,@LQQQQ AaQQQQ PPH0(  >@  7ggD   pw  dMbP?_*+%&?'?(?)?M6HP DeskJet 830C/832CXC od,,LetterDINU"4$2 $$$$"d,,??&U} } }  } $ }  } m } } } m } } I} m } }  } } } }  } } m} } }  p;;;;;;;;   ; ; ; ;;;;J @ J ;J J ;J J ;J J >;jjjjjjjjjjjj N:j N<  Gjjjjjjjjjjjjj  BK  CCBjjjjjjjjjjjjj  G~  H>@  J~ S?jjjjjjjjjjjjj  G HN@7 ZD   G"TLXz?  DAjjjjjjjjjjjjj  G~  HV@  GT@ Djjjjjjjjjjjjj  EH  FFFjjjjjjjjjjjjj  EI  FFFjjjjjjjjjjjjj  EJ  FFFjjjjjjjjjjjj G j G jjjjjjjjjjjj M j BL CCB BN CCB {ss{jjjjjjjj ~ HF@ J~ @ j G~ H>@ G" T;{? D A G~ H>@ G T? D  {{{jjjjjjjj ~ HF@ G @ D  j G HN@ ZD  J SʡE? G HN@ ZD  G& TLXz? D A {{{jjjjjjjj E~ V@ "  H@  D A j G~ HV@ G& T;{?D A G~ HV@ J~ S@ {{{jjjjjjjj F j EH FFF  EH  FFF{sssjjjjjjjj ~ eV@ g"lv @ DAj EI FFF  EI  FFF{sssjjjjjjjj ~ HF@ Glv @ Dj EJFFFD  EJ  FFF{sssjjjjjjjj E~ V@ ~ (@jNDDDD jjjjjjjjjjjj<jjjjjzjjjjzjjjjjjjjjjjjjjjj =j   j   jjj   j   jjj   j   jjjjjjjjjjjjjjj   j   jjj   j   jjj   j   jjjjjjjjjjjjjjj   j   jjj   j   jj B CCB B CCC  B  CCCj   j   jj G,H7x6@DD AbA J~ S@ G,H#UF@ D D AbA J~  S?  f~  dN@  JSʡE?jjjjjjjjjjjj GH!TP@ ZD J~ S(@ G,Hj~F@D D AbA G, T~?D D A  h i>@C ZD   c,T;{? DD AAj   j   jjDl0VJdyJJJH~/p@tt"ttt"tt J !;";#;$;%@&' (J );*J +J ,;-;.;/J 0J 1D23J 4J 5h6;7;8;9;:;;,<;=;>,?x@ G~ HV@ G, T*@DDA G% HV@7DD J S9v? g~ eV@ G, T;{? DDA j    j    jj !E !FFFD !M !FFF ! E ! FFF!j !! ! !j !! ! !jj "E"FFFD "M "FFF " F " FFF"jjjjjjjjjjjj #E#FFFD #M #FFF # E0 # FFF#jjjjjjjjjjjj $E $FFFD $E $FFF $ E $ EEF$jjjjjjjjjjjj>%jjjjjjjjjjjjzzzzjjjjjjjjjjjj &>>&jjjjjjj '@A'j '~ '$@ '~ 'F@ 'jj ( QQ (j (~ ((@ ((y&1@ 4U~ 4V"@ 4U~ 4 VF@ 4 B4 A 4B4A 4B4A 4B4j 44 4 4jj 5G=5TLXz? 'D4D5AAD4AA 5J~ 5SN@ 5U~ 5V&@ 5W=5 X]M M@6 'D5D4 AAD4AbA 5 5 5 "@6D4 5 ],564á@8D5D4 AA 5\O5\\\[5j 55 5 5jj 6G=6T@ 'D5D6AAD5AA 6G%6TV@6D5D4 6W=6XCU)@7 'D4D6 AAD4 AA 6W%6 XR7yS@6D5 D4  6 6 6 "@5 D4 6 A,664á@5D5D4 AA6AAAA6jjjjjjj 7E 7FFF 7^(7_&@D5 7^*7 _R7y^@8 D5  7 } 7 }`` ,764á@6D5D4 AA 7`7"@6 D4 7`7&@DD57jjjjjjj 8E% 8FFF 8^)=8_1(B @8'D6D8 AAD6 AA 8^+%8 _p5C6,@8D4 D7  8  8 AA 8A"8A8"@7D4 8R!8&@7D58jjjjjjj 9E 9EEF 9Y'9ZZZFFF 9jjjjjjj:N :E,0:ZZZFFFDDDDDDDDjjjjjjj ;Y&0;YYZFFDDDDDDDDjjjjjjj <E-0<FFFFFDDDDDDDDjjjjjjj =E/0=FFFFFDDDDDDDDjjjjjjj >Y.0>FFFFFFDDDDDDDDjjjjjjj<?jjjjjjjjjjjjjjjjjjjjjjjjjjjDl~~~B&^bfbhl,:PPl&|<>ZLBBBB@ AJ B;C;DJ EJ F;G;HJ IJ JjKjLJj MJj N;jOjPjQjRjSjTjUjVjWjXjYjZj[j\j]j^j_j @?B@jjjjjj @~ @@ @~ @@ @jj A?Ajjjjjj A~ A@ A~ A@ Ajj BB#BCCCD BB$ BCCC Bjjjjjj BBl12@ B~ Be@ Bjj CGPCH;YXoB@D:DDDEDCDDDEAcA CJ~ CI@ CJCI(\oB@ CGMC HNI@E7DD DE DD DE DCAAACjjjjjjjjjjjj DGPDH1J@E:DCDEDDDCDEAcA DJ~ DK@ DGPDHڥ1J@:DC DE DD DC DE AcA DJ~ D K@Djjjjjj DD D Djj EGPEHV@5 :DCDDDEDCDDAcA EJ~ EK@ EGPEHX1RV@5:DC DD DE DC DD AcA EJ~ E b@Ejjjjjj EE E Ejj FE\FFFFF FE] FFFF Fjjjjjj FF F Fjj GE[GFFFF GE[ GFFF Gjjjjjjjjjjjj HEZHEEFF HEZ HEEF Hjjjjjj HH H HjjIjjjjjj II I IjjJ{ JJ JJ LL LL MM MM NN NND+ ljjHH`L:000`jajbjcjdjejfjgjhjijjjkjljmjnjoj$@,  v(    jA ?? TRI3Picture 2TRI3( #/Q]&`"  jA ?? TRI2Picture 5TRI2 Bb)G]&` "  jA ?? TRI4Picture 7TRI4b ]&`"  jA ?? TRI1Picture 9TRI1}]#]&``"  tA??sinelwPicture 22sinelw &1 ]&` "  pA ?? trirtPicture 23trirt/F]&`"  tA??trinotPicture 24trinot)n/]&`"  |A??a306090nPicture 29a306090n  ]&`` "  xA ??a4545noPicture 30a4545noo=]&` ">0@  DDD7ggD  Oh+'0@H`p agnes azzolinoUserMicrosoft Excel@ s@ʽ|"՜.+,0 PX|  MATHEMATICAL CONCEPTS, inc. introsolve triangle  Worksheets F&Microsoft Office Excel 2003 WorksheetBiff8Excel.Sheet.89qCompObj r