Topo 1
August 8, 2022 | Author: Anonymous | Category: N/A
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ING. GAUDENCIO GALVEZ CHOQUE 3ra Edición Huancayo - Perú ayo - !""#
CON$ENIDO.
UNCP-FACULTAD DE MINAS
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ING GAUDENCIO GALVEZ CHOQUE
AGRADECIMIENTO INTRODUCCION GLOSARIO CAP.I. %.-$EO&IA DE E&&O&E'.
- EXACTITUD - PRECISION. 1.1.
ORIGEN DE LOS ERRORES.
1.2.
CLASES DE ERRORES.
1.3 .3..
VALOR PRO PROBABL ABLE SIM IMPL PLE E.
1.4 .4..
VALOR PRO PROB BABL ABLE PON PONDE DER RADO DO..
1.5.
MAGNITUD DE ERRORES.
1.6.
ERROR PROBABLE.
1.7 .7..
ERR RRO OR PPRO ROB BAB ABL LE PO PONDE NDERA RADO DO..
!. O&IE O&IEN$ N$A ACI(N CI(N D DE EP PLA LANO NO'. '.
2.1.
RUMBOS.
2.2.
AZIMUTS.
2. 2.3. 3.
CO CONV NVER ERSI SIÓN ÓN DE RU RUMB MBOS OS-A -AZI ZIMU MUTS TS Y VICE VICEVE VERS RSA. A.
2.4.
NORTE MAGNETICO.
2.5.
DECLINACIÓN MA MAG GNETIC ICA A.
3. E'CALA'.
3.1.
ESCALA NUMRICA
3.2.
ESCALA GRA!ICA.
). EDI EDICI CION ON D DE E DI DI'$ '$A ANC NCIA IA'. '.
4.1.
MEDIC ICIO ION N DIRECTA.
4.2.
MEDIC ICIO ION N IN IND DIR IRE ECTA.
#. EDI EDICI CION ON DE ANG NGUL ULO' O'..
5.1 .1..
ANG NGUL ULOS OS POR REPE REPETI TICI CIÓN ÓN..
5.2 .2..
ANG NGUL ULOS OS POR REIT REITE ERA RAC CIÓ IÓN. N.
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ING GAUDENCIO GALVEZ CHOQUE
CAP.II %. POLIGONACI(N.
1.1. POLIGONAC POLIGONACIÓN IÓN CERRADA. CERRADA. 1.1.1. MEDICION DE LADOS. 1.1.2. MEDICION DE ANGULOS. 1.2. CONSTRUC CONSTRUCCIÓN CIÓN DE POL"GO POL"GONOS. NOS. 1.2.1. POL"GONOS POR DESVIACIÓN O DE!LEXIONES. 1.2.2. POLIGONOS POR AZIMUTES. AZIMUTES. 1.2.3. POL"GONOS POR ANGULOS ANGULOS INTERNOS. !. E&&O E&&O& & DE CIE CIE&& &&E EA ANG NGUL ULA& A& * LI LINE NEAL AL..
2. 2.1. 1. ERRO ERROR R DE CIE CIERR RRE EA ANG NGUL ULAR AR.. 2. 2.2. 2. ERRO ERROR R DE DE CIE CIERR RRE EL LIN INEA EAL. L. 2.2.1. ERROR RELAT RELATIVO. 2.3.. CLA 2.3 CLASI! SI!ICA ICACIO CION N DE UNA POLIG POLIGONA ONAL L POR SU ERROR RELA RELATIVO Y ANGULAR. 2.3.1.
COMENTARIO.
3. COP COPEN EN'A 'ACI CI(N (N ANG ANGUL ULA& A& * LI LINE NEAL AL..
3.1. COMPENSACI COMPENSACIÓN ÓN ANGUL ANGULAR. AR. 3.1.1. POLIGONAL CERRADA. 3.1.2. POLIGONAL ABIERTA. 3.2. COMPENSACI COMPENSACIÓN ÓN LINEA LINEAL. L. ). CALC CALCUL ULO O DE AZI AZIU U$' $' * COO& COO&DE DENA NADA DA'. '.
4.1.. AZIMUT 4.1 AZIMUTS. S. 4.2. COORDENADA COORDENADAS. S. #. CAL ALCU CULO LO DE C CO$ O$A A'.
5.1. METODO METODO GEOMT GEOMTRICO. RICO. 5.2. METODO METODO TRIG TRIGONOME ONOMETRICO TRICO.. CAP III
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ING GAUDENCIO GALVEZ CHOQUE
1.- AL$IE$&IA. 1.1 .1..
NI NIVE VELA LACI CIO ON TOPOGR# OGR#!I !IC CA.
1.2 .2..
PR PRIN INCI CIPI PIO O DE NI NIVE VELA LAC CION. ION.
1.3.
TIPOS D DE E NI NIVELACION.
1.4.
NIVELACION GEO GEOMTRIC ICA A. 1. 1.4. 4.1. 1. NIVE NIVELA LACI CION ON SI SIMP MPLE LE.. 1. 1.4. 4.2. 2. NIVE NIVELA LACI CION ON COMP COMPUE UEST STA A. 1. 1.4. 4.3. 3. NIVE NIVELA LACI CION ON REC RECIP IPRO ROCA CA.. 1.4. 1.4.44.
COM OMPE PENS NSAC ACIÓ IÓN N.
1. 1.4. 4.5. 5. ERRO ERROR R M#XI M#XIMO MO PER PERMI MISI SIBL BLE. E. 1.5 .5..
NI NIVE VELA LACI CIO ON TR TRIG IGO ONOME NOMET TRI RICA CA..
1.6 .6..
NI NIVE VELA LACI CIO ON BARO BAROM MT TRI RIC CA.
1.7.
LIBRETA DE CAMPO.
1.$.
CURVAS D DE E NIVEL. 1.$. 1.$.11.
E%UI E%UIDI DIST STA ANCI CIAS AS..
1.$.2. 1.$ .2. CARACT CARACTERI ERIST STICA ICASS DE DE LAS LAS CURV CURVAS. 1.$.3. 1.$ .3. METODO METODO PPA ARA GRA GRA!IC !ICAR AR CU CUR RVAS DE NIVEL. NIVEL. 1. 1.&. &.
PER! PER!IL ILES ES LONG LONGIT ITUD UDIN INAL ALES ES Y TR TRAN ANSV SVES ESAL ALES ES..
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ING GAUDENCIO GALVEZ CHOQUE
AG&ADECIIEN$O E' ()( ()(*+, *+, ,+*'/ ,+*'/0+ 0+ +* ,' ( ( , '( * *8+ 8+(( ,9( ,9( +,+,* +,+,* ( (9 (99 9 (00(*(9: + ;*( (: ?+*+9 ,9*(',9: ,* +('( , +,*, , '( !(+;'( , I*0,*,>( , M*(9 , '( U*),9( N(+*(' ,' C,* ,' P,@ (0(,+ ( 9 '9 ;, ((* ,* '( ,'(=(+/* ,' ,9,*, (*;(' +* ,' '(*,(,* , '9 =',(9: ,,++9 ,* '( (0((+/*: ,+/*: (9> 9 ( '9 ;, (;,* , * ,+';9)(,*, (( '9 ,9;(*,9 , '( !(+;'( , M*(9 ;, ;, ;* (, , 0(* ,*),0(;(: )9 '( (+0( *9 )9 ,* '( *,+,9( , ,( '( 9,0;*( ,+/* +* +,(9 +(+*,9 +* =',(9 : ,9, '( ,+( * , ,,(9 ,(9 ,* ,'(=( '( 3( ,+/*: P(( ;*(,*( , ,' +;9 9, ( (( ,9(''( *;,)9 ,'9 (,8+9: ,9 , 9 *9 ,8 ,('( ('09: (( ,' +(9 ,9,+>+ ,' +;9 9, ,9(''(8 (9 ( (9 + '',0( (' ,9;'( *(' ,' =',(. E* ,' ,9,*, , *9 +;(,9 ,+';9)(,*, (' ,9('' 8++ ,' +;9: *+(* ;*( POLIGONACIÓN ';,0 ,('( '( NIVELACION: 9(=,* ;, (( ( 0,*,(' 9; *(;(',( 9, ;*( +,*+( ('+(( ;, 9, ,*+(0( , ,,*( '(9 9+*,9 ,'()(9 / (=9';(9 , '9 ;*9 9=, '( ,(: ,' 9 ;, ,9;( '9 ?9 +,,*9 (( ,('( '(9 ,+*,9 9=, ,' ,,* 9; ,,9,*(+/* 08+(: (( ,'' ,9 *,+,9( +*+, ('0;*(9 ,*+*,9 (( ,*,*, ,' +*,* ,' +;9 %.- A'$&ONO A'$&ONOIA. IA.- C,*+( ( * ( '( 0(> 0(>(( ;, *9 ,, ,, ,'(+*( ,'(+*( '( 9+/* 9+/*
, '( ,( +* 9 (99 ' (* ;=+( '9 ;*9 9=, '( +,( ,,9,. !.- AZIU AZIU$ $.- E9 ,' 8*0;' ( >( ,*, ,*, =(9 =(9(* (*, , ,' ,'(+ (+/ /** +* +* '( T0 0(> (>(( ).- CA& CA&$O $OG&A/I G&A/IA. A.- L( +( G,,9(: P ;, '( +(0(>( *9 ( '( ?+*+( + ,,9,*( '9 '(*9 9=, ;*( +(( / ((: ,* )9( ;, '( ,( ,9 ;*( 9;,+, +;)( ;09(: (( ,'' ;'( ?9 ((9 , ,++*,9 (( 0(+( ;* '(*. #.- CENI$.- E9( ;=+( ,* ,' '(* ),+(': ,* ,' +;(' (( , 8*0;'9 ),+(',9 ,'
0,* / FH ,9( ;=+( ,* '( (, 9;, ,' =9,)(. 0.- CONVE&GENCIA DE E&IDIANO.- P(( *+( +,,* , +8'+;'9: 9,
+*+, ,' N, M(0*?+: ),(, U.T. U.T.M. M. ,**+,9: +*),0,*+( , ,(*9 ),*, ( 9, ,' 8*0;' ( '( '>*,( ;, *+( ,' N, ),(, ,' N, +;(>+;'( / U.T.M.
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ING GAUDENCIO GALVEZ CHOQUE
1.- COO&DENADA'.- L(9 +,*((9 ),*,* ( 9, '9 ,,9 X , Y: ;, 9, , ((
,,9,*( / 0(+( '9 '(*9 ,* ;*+/* ( 9;9 +;((*,9. 2.- CU&VA' DE NIVEL. - D,**( (=?* + +;)(9 *,(9 ;,
;*,* '9 ;*9 ;, 9, ,*+;,*(* ( ;*( 9( (';( / ,',)(+/*: ,9 , (*+( (( ,,*( '( +((+,>9+( >9+( ,' ,,* ,' 9 ;, 9,)8 (( ,('( '9 ,+9 , *0,*,>(. .- DECLINACION AGNE$ICA . S, +, ;, '(9 (0;(9 , '( =@;'( 9,, *+(*
'( ,++/* , '(9 '>*,(9 (0*?+(9 ,,9,: '9 99 ;, * +*+,* +* ,' N, ),(, / >9+ , '( ,(: ' ;, ,' ' (0*?+ ,*, ( )(( ,* ,' (*9+ ( *9+;9 ;9 ,' , ,:: ,* ,**+ *+,9 ,9 '( ,+ ,+'* '*(+/ (+/** (0*? (0*?+( +( ),*, ),*, ( 9, ,' 8*0;' 8*0;' ( ,' N, M(0*?+ M( 0*?+ ,' N, V,(,. V,(,. %".- DIAE$&O ECUA$O&IAL.- D9(*+( ((( ,9 12756:776 ,9. %%.- DIAE$&O POLA&.- D9(*+( , ' ( ': 12714:F47 .
((.
%!.- DIUO.- P+,9 ;, +*99, ,* ,,9,*( 08+(,*, ,* ,' (,' '9 (9
(9 ,* +( ( ;*( ,9+('( ,,*((. %3.- DI'$ANCIOE$&O.- I*9;,* ;, 9), (( , 9(*+( ,(*, (9
'(9, +* ,' ( , (9. %).- ECLIE$&O.- I*9 I*9;,* ;,* 08+ 08+ ; 9,*+' 9,*+'' ' ;, 9, ,)( ,' *),': ,* ,'
;, +;' 0(;(: ,* ,' +;(' 9, ;,, ',, '9 8*0;'9 9,(0,9(',9 , (+;, ( '( *+'*(+/*: '( 0(;(+/* 9, *+( ,* ,' +,* ,' 9, +>+;' +* FH *,(9 , ,++/* ( ;*(
9( (';(: ,,*( '( ,,*+( ),+(' ,*, 9 ;*9 +* ,' ( , '(9 (9 ,9(?+(9: ,* , '9 N),',9 9, 9*0;, *),',9 , =;=;(: , +8((: , (*, , *0,*,: ,*, 9. !#.- PLANIE$&O.- I*9;,* 08+ ;, 9), (( ,,*( ,' 8,( , ;*
,,*: ;, +*99, ,* ;* =( ',=', ,* , * ,' ,, ,*, ;*( (0;( +* ,' +;(' 9, ,+, ,' ,>, ,0;'( ,' ,,* ( +('+;'( (' ,, ;,9 ,*, ;* (= 0(;( ,* ,' +;(' 9, =9,)( ,' *@, , );,'(9 ;, (: ( ;*( ,9+('( ,,*(( 9, +('+;'( ,' 8,( ,(*, / /;'(9. ;'(9. !0.- PLOADA.- E9 ;* *9;,* 08+ 89 9,*+'' / (' ), ,' 89 (*0;: 9;
,9 0,*,(',*, 9+'( ,*, 2FF ( 3FF 0. E9 ;'( (( (=(9 ,9,+(',9 J0(>( S;=,8*,(K 9, ,',(* '((9 ,9, 5 ( $ 0 , ,9. !1.- PUN$O' $OPOG&A/ICO'.- S* ;*9 >9+9 ;, 9, (,('(* 9=, ,'
,,* ,9, '9 +;(',9 9, *+( '(9 ,+ ,,* ,+*,9 *,9 , 9(*+(: 9(*+(: 8*0;'9 ( 9, ( ( ,,9,*(
'9 '(*9 (( ;*( =;,*( *,,(+/*. 3).- 5INCHA.- E9 ;*( +*( 0(;(( ,* +,*>,9 / ;'0((9: 9),* (( , '(9
9(*+(9 ,*, 9 ;*9: ,98* (=+((9 , '*(: (+,: =( , ): (( (=(9 08+9 ,98* 0(;(9 ,,(;(: ,*9/* '*0; ),(,(: ),*,* +*(9 , 1F: 2F: 3F 3F:: 4F: 5F 9 , '*0;.
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ING GAUDENCIO GALVEZ CHOQUE
CAPI$ULO I
%. $EO&IA DE E&&O&E'.
D,* , '(9 ,+*,9 ;, ,('( ,' /0(: ,9( ='0( ( +*+, '9 , ,,* ,*, ,99 , , ,9 ,9 9 9=' =',9 ,9 ;, ;, 9, ;, ;,(( +, +,, , ,* ;*( ;*( ,*9 ,*9; ;(: (: 9,* 9,* '( ,9*9(='( ,' /0( (*,*, ;*( ,+/* ,* , '9 '>,9 ,9=',9 , ,+ ,+9 9/ /*: *: (( (( ,'' ,'' ,9 *,+,9 *,+,9( ( ;, ;, +* +*+ +(( '( '(99 +(; +(;9( 9(99 , ' '99 , ,, ,9: 9: ,9 (*, ,*, ,9,*, '( ,,*+( ,*, ,+9/* ,(+;. - E6AC$I$UD.- E9 '( ((+/* (=9';( ( '( ),( JS+,( A,+(*( ,
I*0,*,9 +)',9K T(=?* 9, ,*, + ,' 0( , +*( +* ;* (/* / ,' JS,)+9 G,?9+ , +9( , '9 EE.UU.K. - P&ECI'I(N.- E9 ,' 0( , ,,++/* +* ;, 9, ,('( ;*( ,(+/* D,
(=(9 ,*+*,9 ,9 +*+'; ;, ;*( ,+/* ;,, 9, , 0(* ,+9/* +* ( '(9 ;*(,9 *,+,9((9 * 9, ,(+( / )+,),9(.
%.%. O&IGEN DE LO' E&&O&E'.
- E&&O&E' HUANO'.- D,* , ,'' ,*,9 '(9 '(+*,9 , '9 9,*9 J)9(: (+: >K '( ,(+/* *+,+(. - E&&O&E&' IN'$&UEN$ALE'.- C(;9(9 '9 (;9,9 ,,+;99 +('=(+*,9 ,/*,(9 , '9 ,;9 08+9. - E&&O&E' PO& /ENOENO' NA$U&ALE'. - S* +(;9(9 (++/* ,,,'/0+(: + '( ,,(;(: ),*9: ,(++/* ,,9,: ( , ,,9 ,9 ;* ,( (': ' ;,
,*+( ,* +(, ,9 9 9' 9'(, (,*, *, ' *,+ *,+,9( ,9( (( (( ('+( ('+( ,* ,' +;9 +;9 , T0( 0(>(: >(: ,*,*,* '( (0*; , ,,9 + ,' (( ,' , ;, 9, +,, ,* ;*( ,+/*. %.0. E&&O& P&OALE.- V,*, ( 9, ;*( +(*( 9)( / *,0()(: ,* ,
,9 ,999 '> '>, ,99 ;, ;,,, ,*+ ,*+* *( (9 9,, ,' , , 89 89 = =(= (=', ',:: (( (( ,' ,'' ' (, (, 99 ,+(,*, '(9 /;'(9 , ('+(+/*: =)(* 9; ,9(+/*.
1K
E =
F.6745σ
2K
E =
3K
E =
4K
E = V
σ
=
Σ v
2
n−1
F.$45 Σ v n
J
n −1 K
F.$45 V
S E E =(=', =(=', σ ,9)(+/* T>+( Σ)2 S;(( ,' +;(( , '(9 ,9)(+*,9.
Σ) S;(( , '9 )(',9 (=9';9 , '( V
,9)(+/*
M,( , '( ,9)(+/*.
) D,9)(+/*. * N@, , =9,)(+*,9. E7e89+o 0.
S, *,( WP% 9(=,* ;, ,' R;= M(0*?+ ,* 1&55 ,( , S32H4FE 9; ,+'*(+/* (0*?+( 7H35E: ,,*( +;(' ,9 ,' R;= ),(, ,' R;= (0*?+ (+;(': 9 '( D,+'*(+/* (+;(' ,9 2H2F. 'OLUCION;
R S 32H4FE 32H4FE JR;= (0*?+K DM1&55. 7H35E
'.V.
2001
1955
W 2 0 2 !
% M 1
1 0 2 0
9 95 5
% M
7 ! 3 5 0 E
1 5 1 7 5 ! 1 1 4 5 4 ! 0 5 7 ! 2 0
W
5 0
E "4m6t 2001
P
"4m6t Ved8de "4m6t 1955
+
3
Z (0*?+ (( 1&55 ,9 Z 1$F 32H4F 147H2F E' ZV ZM DM55. ZV 147H2F 7H35 154H55 R;= ),(, R V 1$FH - 154H55 ' !#*,( ,+( 9, , 7.5 . 9, ;,, =;( ,* ;* (,' A3: ,,*( ( ;, ,9+('( 9, =;(8.
'OLUCION.
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ING GAUDENCIO GALVEZ CHOQUE
31
1 P = E T
1E T 7.5 . P T(( ,' (,' A3 ,9 42F 2&7 . E' '(0 ,' (,' ,9 42 +. P(( =;( ,9+*(9 '9 80,*,9 1.5 ( +(( '(: (' 3 +. E**+,9 ,' (,' ,*8 ;* (( , 42 3 3& +. L;,0:
1 E
=
39:m 7.5m
< E = 19230 .77; xm. 2000 F
P(( ,('( '( ,(+/* (=(9 +(*(,9 ,=,* ,9( ,* '( 9( ;*(. E**+,9 '( ,9+('( ( =;(9, ,=, 9, 12FFFF. NO$A C;(* C;(* WE ,9 ;*( +(* +(*( ( ,,*, ,,*, ( '( ,9+('( +*+ +*+(: (: 9, ,* ,*,( ,( (
;*( +(*( *,(( 9;,: (' + 2FFFF 3.!. E'CALA G&A/ICA E9 ;*( ,+( ) )(( ,* (,9 0;(',9 ;, ,,9,*( ,,9,*( ;*( +/* , '*0; , ,,* ,* ;* ((: A9> ,,' ,* ,' 08+: 1 +
,,9,*( ( 1FF . D,9, ,' ;* F . 9, 9;=), 0* , 1, ,* , 5 '(9 ,' , 8 ,9=', 9,8 f 15\J5K12 33.54\: 90*+( ;, ,* ;* ,*80* ,' , (*0;'( 8 ,=, 9, 33.54 (( , +,*9(: +(9 +*(: 9 ,9 ( 9, );,'), ( ,('( ,' (=( , +(: +* ,' 9 +, (( ,' 2: 3, 4 ,*. L( +;(( +';*( *9 +, '( ,+9/* ,' ,' ;, ,=, ,=, 99 , ,' ',( ,( (( (( *;,9 *;,9 9 9 ', ',)( )(* *( (,* ,* 9: 9: '( @' @' (( +'; +';* *(( ,+,*( ;? ? , ,+/* ,=, ;9(9,. P&IE& O&DEN.- L,)(*(,* , 0(* ,(+; + (( +((9
;=(* ; , 0;(' (*+(: '9 8*0;'9 ,=,* ',,9, ,,(+/* , ,9 ( +;( 9,,9 +* ,'9 , ((+/* ( '9 5 (( , '9 '(9 '(9 9, ,9 ,9,+( ,+( '(9 ,* ,*,* ,*,9 ,9 ^ 1h: (( (( ,*, ,*,*, *,99 (,9 (,9 ;'(9
9
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+
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48
2 ( 3 9,,9 +* ,' , ((+/* ( '9 2F (( , 9;9 '(9 9, ,9,+( '(9 ,*,*,9 ^ 2h: (( ,*,*,9 (,9 9, , 9=, '( 9;,+, ,' ,,* (( ,9;?9 9 ,,+ ,,+/* /* 1 ( 2 9,,9 +* , ,'9 '9 , ( ((+ (+/* /* ( '9 3F: 9;9 '(9 ,=,* 9, ,9 ,* , '9 2h , ,*,*, (,9 ( ,99 ,=,* ,0(9 ( '( 9;,+, (( 9; 9, +,++/*. CUA&$O O&DEN.- P(( (=(9 ,'*(,9 ,99 ,=,* 9, ,9
,,+/* 1 9,, +* ((+/* (' 1] 9;9 '(9 ,=,* , 9, ,9 ,* ,' 3h , ,*,*,. 3. COPEN'ACION ANGULA& * LINEAL 3.%. COPEN'ACION ANGULA& 3. 3.%. %.%. %. PO POLI LIGO GONA NAL L CE CE&& &&AD ADA A.- L( +,*9(+/* (*0;'( '( ,9 +
+*9,+;,*+( , '9 ,,9 (*0;'(,9 ,' +;(' 9, +,*9( ,(*, '(9 +* +*+ +(9 (9 , ,( (, ,99 0, 0,? ?+ +(9 (9:: ,' , , (*0; (*0;'( '( 0*9 +,(9: ,* )9( ;, '9 '>0*9 (=,9 (' *+ (' *(' * ;,,* ,+9(9, 9;9 +,*((9 , +=(+/*: 9(') ;, ,9?* ,*'((9 ( ;*9 , (*0;'(+/*: ( *0;'(+/*: ,*(9 ;, ,* '(9 '0*(',9 +,((9 '(9 +,*((9 , ((*;, ,=,* 9, 0;(',9 ( '(9 +,*((9 , +,,: 9> ,' , , +,, '*,(' ,9
Er . L =
∆ X
2
2
+ ∆ Y
E' E.L. E.L. ,=, 9, +,: ,**+,9 (( + +,*9( ,*9( '( '*0; JbXK '(; JbYK 9, ,*, ;,
!+.C bX
!+.C bY
D*, !+.C !(+ , +,++/* ,* ,' ,, X !+.C !(+ , +,++/* ,* ,' ,, Y bX D,,*+( , 9(*+( ,* ,' ,, X J'*0;K bY D,,*+( , 9(*+( ,* ,' ,, Y J'(;K P P,>,
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58
L;,0 '( +,*9(+/* 9,( C: /c.C: : d
Cy /c.Cy : d
D*, C V(' V(' ( +,*9( ,* ,' ,, X C V(' V(' ( +,*9( ,,** ,' ,, Y 9(*+( ,' '(. E9, )(' ,=, 9, 9;( ('0,=(+(,*, ( +(( '( ,* 9; '*0; '(;: , (' (*,( ;, '( 9;( (' , '(9 +,* +,*((9 ((9 (+(' (+(',9 ,9 ,=, 9, +, ,*, ,' , '*,(' 9,8 +,. ).- CALCULO DE AZIU$ * COO&DENADA' ).% AZIU$. P(( +('+;'( ,' (; , '9 '(9 ('+(9 '( ,0'( , '( *,/*+(
+,,* ,+8*+ ,* 9,* (* 0* , (+; (+;, , ( +;9. N ZAB 115H ∠A 54H B 133H C 226H D 55H E 72H
A
E
C D
'OLUCION;
D, (+;, ( '( ;'( *,/*+( 0*: *: ,,*+( ),+(': c (';( , *9;,*: d (';( , 9,(' e +( ,' ;*.
%".- Diu7o de 9+ano.- P(( P(( =; =;( ( ,* ;* 99 99,( ,( , +,* +,*(( ((99 9, =;9+( ,'
(*0 ,* ,' ,, N, E9, (( ( '9 ',9. P(( ,*+*( '9 (*09 9, ,9( '9 )(',9 ,,9: ,* +(( ,,. S,0;(,*, 9, 0*.
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67
E 5FFN A 45FN
B D
4FFN
E F F 7 C E F 5 7
E F F $
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ING GAUDENCIO GALVEZ CHOQUE
68
CAPI$ULO III %. AL$IE$&IA.
E9 (, , '( 0(>( ;, (;( ( ,,*( '(9 (';(9 ,'()(9 (=9';(9 , '9 ;*9 08+9 9=, ,' '(* ),+(': ,(*, ,' +,,* +*+ + *),'(+/*: ,' 0,* (( ;=+( ;*( (';( 9, (/ ,' *),' , ,' (: ''((* (';: (';( (=9';( +(: (( ,+*,9 08+(9 +. 322F
C
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3215
E 3212 B
321F
D
32F$
E$ODO G&A/ICO.
P(( (( '(9 +;)(9 ( '( 9( (';( 08+(,*, ('+(9 ,' *+ , '( )9/* , ;*( ,+( ,* (,9 0;(',9. E* ,' +;9 '9 ;*9 A B ;*9 +* ;*( '>*,( ?=': ( ( ,' ;* A ((9 ;*( '>*,( (;'( (' + AB: ,* ?9( ((9 '(9 ,;9(*+(9 , (+;, (' ,;,,* (' + 5 9 , +;)( ( +;)(: ,,(9 ,* '( +( 3225.9.*... ,* ( ,9+,*,*,: 322F: 3215: 321F: ,' @' 3225.9.*. @' ;* 0(+( ,* '( ,+( (;'( ;*9 (' ;* B: ((9 ((','(9 ( 9;9 ,9,+)(9 (';,9 ,* '( *,9,++/* ,9 '( (';( ;, ', +,9*,. E$ODO ANALI$ICO.
L9 ;*9 CD ;*9 +* ;*( ,+( ?=': ,* ,''( ,('(9 ' 90;,*, - M, M,99 '( 9(*+ 9(*+( (
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