excelencia geo 2012 02 angulometria

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  • 7/31/2019 Excelencia Geo 2012 02 Angulometria

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    LVBLKLEBGI4194

    QTJNLRJT?Ltgbc ^ry|lz Kkiejr IRGHEI]\TI? NLBFI? 9= 18 4194

    E 14- IEH\KJ@L]TGI TLB]IR QITIKLKIR BJT]IMIR QJT \EI RLBIE]L EH\KJR LE \E ]TGEH\KJ

    19% EH\KJ? Lr ki tl|ege ml mjr tiwjr y|l }glele |eq|e}j lv}tl`j bj`e+ lr mlbgt }glele lk `gr`jjtghle%Kjr mjr tiwjr rje kjr kimjr mlk eh|kj w lk q|e}jlv}tl`j bj`e rl kki`i ^T]GBL mlk eh|kj%

    I

    DJ

    9%9% Lkl`le}jr mlk eh|kj%

    9% Kimjr? JI w JD

    4% ^t}gbl? J

    2% Rg`djkjhi? IJD+ IJD3 IJD

    =% Ej}ibge? IJD 0 JI JD

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    m' eh|kj Tlb}j? Lr iy|lk eh|kj b|wi `lmgmi lrgh|ik i 71

    l' eh|kj E|kj j Qlthjej? Lr iy|lk eh|kj b|wi`lmgmi rl bjergmlti gh|ik i 1%

    I

    DJ

    0 1IJD`

    =%4% RLHE KI QJRGBGE ML R\R KIMJR

    i' eh|kjr imwible}lr?Rl mgbl y|l mjr eh|kjr rje imwible}lr b|iemj }glelelk `gr`j ~t}gbl w |e kimj bj`e }ik y|l kjr kimjr rlleb|le}tle i j}tj w j}tj kimj mlk kimj bj`e%

    DJ

    kimj bj`e

    I

    B

    d' eh|kjr bjerlb|}g~jr?

    Rl mlej`geie ir mjr j `r eh|kjr y|l rjeimwible}lr bje r|r ge`lmgi}j%

    b' eh|kjr jq|lr}jr qjt lk ~t}gbl?

    Rje mjr eh|kjr ml}lt`geimjr ik }tizit mjr tlb}irrlbie}lr%

    m' eh|kjr imwible}lr bj`qkl`le}itgjr?Rl mgbl y|l mjr eh|kjr rje imwible}lrbj`qkl`le}itgjr+ b|iemj }glele lk `gr`j ~t}gbl wb|wjr kimjr }glele lk `gr`j ~t}gbl w b|wjr kimjr ejbj`|elr njt`ie |e eh|kj tlb}j%

    l' eh|kjr imwible}lr r|qkl`le}itgjr?Rl mgbl y|l mjr eh|kjr rje imwible}lrr|qkl`le}itgjr+ b|iemj }glele lk `gr`j ~t}gbl wb|wjr kimjr }glele lk `gr`j ~t}gbl w b|wjr kimjr ejbj`|elr njt`ie |e eh|kj tlb}j%

    n' eh|kjr le}tl Tlb}ir Qitiklkir

    Rlie kir tlb}ir ` w e tlb}ir qitiklkir bjt}imir qjt |ei

    tlb}i rlbie}l + k|lhj }lel`jr?

    `

    e

    9 4

    2=

    > = 6 2 8

    9%2% eh|kjr Bjeo|himjr j Bjki}ltiklr

    eh|kjr Bjeo|himjr Ge}ltgjtlr?

    `= `< 961 `2 `< 961

    # 0

    # 0

    9%=% eh|kjr Bjeo|himjr Lv}ltejr?

    `9 `6 961 `4 `8 961

    # 0

    # 0

    JDRLT^IBGE?

    i' B&B&B&B&B B& ''''' 0 + rg e lrqit0 B&' + rg e lr g qit

    d' R&R&R&R&R R& ''''' 0 + rg e lrqit0 R&' + rg e lr g qit

    Qtb}gbi ml bkirl

    9% Rg i |e eh|kj rl kl tlr}i r| bj`qkl`le}j+ tlr|k}i

    gh|ik i ki b|it}i qit}l ml r|r r|qkl`le}j% Fikkit ki

    `lmgmi mlk eh|kj%

    i' 92

    8% Bjergmltiemj y|l lk IJD `gml 9 l' =1

    6% Rl }glele kjr eh|kjr bjerlb|}g~jr+ IJD+ DJB w

    BJM ml `jmj y|l?

    `IJD # `DJB 0 961

    `DJB # `BJM 0 71

    Bikb|kit ki `lmgmi mlk eh|kj y|l njt`ie kir

    dgrlb}tgblr ml kjr eh|kjr IJD w BJM

    i' 71 d' 91< b' 941

    m' 911 l' 92

    99% Rl }glele kjr eh|kjr bjerlb|}g~jr IJD+ DJB w BJM

    ml `jmj y|l?

    &`IJD'&`DJM' # &`IJB'

    &`BJM' 0 &`IJM'&`DJB' w

    &`IJD'&`BJM' 0 c

    Bikb|kl ki `DJB

    i' c4 d' c4 b' c2

    m' c2 l' c

    94% Mlk htngbj+ fikkit lk `iwjt ~ikjt le}ltj qit ml w

    i' 61 d' 64 b' 6=

    m' 61 d' 9>4 b' 9>2m' 9>= l' 9>

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    96% Le ki rgh|gle}l ngh|ti kir tlb}ir ej qitiklkir? K9 w

    K4 njt`ie |e eh|kj y|l `gml 2% Fikkit lk `iwjt

    ~ikjt ml

    i' 9< d' 44 21 b' 969>1 d' 1

    m' 9

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    8% Ki r|`i mlk r|qkl`le}j w lk bj`qkl`le}j ml ki

    `lmgmi ml |e `gr`j eh|kj+ lr gh|ik i e ~lblr lk

    r|qkl`le}j ml ki `lmgmi ml mgj eh|kj% Bikb|kit r|

    `lmgmi%

    i'

    & '#

    71 e 9

    e 9 d'

    & '

    =< 4e 9

    e 2

    b' & '

    7 1 4e 2

    e 4m' & '

    #

    >1 e 4

    e 9

    l'#

    71e

    e 9

    6% Rl }glele kjr eh|kjr bjerlb|}g~jr IJD+ DJB w BJM

    }ik y|l 0` IJM 71 w # 0` IJB ` DJM 941

    m'

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    9>% Rg ` ** e w lk eh|kj LYQ lr ih|mj% Bikb|kit lk

    `lejt ~ikjt le}ltj ml v

    i'

    m' == l' =2

    98% Ml ki ngh|ti+ bikb|kit v% Rg # 0 411 w

    9 4 2K * * K * *K

    i' 91 d' 96 b' 41

    m' =1 l' l' 96

    97% Rg

    9 4K * * K % Bikb|kit lk `vg`j ~ikjt ml v

    i' =4 d' =2 b' ==

    m' => l' =8

    41% Ridglemj y|l? %

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    EH\KJR LE LK ]TGEH\KJ

    9%9%eh|kj njt`imj qjt mjr dgrlb}tgblr ge}ltgjtlr

    9%4% eh|kj njt`imj qjt |ei dgrlb}tgz ge}ltgjt w|ei dgrlb}tgz lv}ltgjt%

    9%2% eh|kj njt`imj qjt mjr dgrlb}tgblr lv}ltgjtlr

    9=% Qtjqglmim mlk b|imtgk}ltj Bebi~j%

    Le }jmj b|imtgk}ltj bebi~j rl b|`qkl kjrgh|gle}l?

    9%% Rg IM w BM rje dgrlb}tgblr ml kjr ;r I wB le}jeblr?

    9% 8% ]ljtl`iLe }jmj ki dgrlb}tgz lv}ltgjt ml |e ; w kiqtjkjehibge mlk kimj jq|lr}j njt`ie |e eh|kjb|wi `lmgmi lr?

    9% 6% ]ljtl`iRg? DB w MB rje dgrlb}tgblr+ le}jeblr?

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    QTIB]GBI ML BKIRL

    19% Rl }glel lk }tgeh|kj IDB+ k|lhj rl }tizi ki ik}|ti

    DF% Le lk }tgeh|kj DFB rl }tizi ki dgrlb}tgz

    ge}ltgjt DT % Bikb|kit FT+ rg ID 0 91 w IF 0 8%

    i' 4 d' 4+< b' 2m' 2+< l' =

    14% Le |e }tgeh|kj IDB rl ridl y|l? `D 0 >1 w

    `B0 94% Fikkit ki `lmgmi mlk eh|kj y|l njt`ie

    le}tl r kir ik}|tir }tizimir ml kjr ~t}gblr D w B%

    i' =1 d' 61 b' 84

    m' l' >4

    12% Le |e }tgeh|kj IDB rl ridl y|l `I - `B 0

    2>% Bikb|kl lk eh|kj njt`imj qjt ki dgrlb}tgz ge}ltgjtmlk eh|kj IDB w ki `lmgi}tgz mlk kimj IB

    i' 7 d' 94 b' 96

    m' 4= l' 2>

    1=% Le |e }tgeh|kj IDB? `D 0 61+ ki `lmgi}tgz ml kiik}|ti DF bjt}i i DB le N% Lebje}tit `DIB+ rg`DNF 0 61%i' =1 d' % Bikb|kit v rg IM lr dgrlb}tgz mlk eh|kj DIB+

    iml`r MB 0 BL

    i' 21 d' 2> b' =1

    m' == d' =6 b' 24

    m' 81 l' >1

    16% Le ki ngh|ti% Fikkit wv # ?

    >7

    v

    w

    i' 4=7 d' 4

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    99% Le ki ngh|ti+ fikkit v%

    i' 9

    m' 9== l' 9=6

    9=% Le ki ngh|ti rgh|gle}l+ fikkl v

    i' =1 d' =1 l' 81

    9

    1=% Le lk }tgeh|kj IDB grrblklr lk eh|kj mlrgh|ik D

    `gml =>% Rl }tizi ki ik}|ti IF % Fikkit ki `FIB%i' 41 d' 42 b' 4=

    m' 21 l' 2>

    1

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    1>% Bikb|kit v rg 0 911BDI

    i' 21 d' =1 b' =1

    18% Le ki ngh|ti+ fikit v

    i' 941 d' 9== b' 92>

    m' 9>= l' 9=6

    16% Le ki ngh|ti+ bikb|kit v

    i'