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Aˆ + Bˆ + Dˆ = 200 g B = 200 − ( Aˆ + V ) %
5
!
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( D AB )UTM = 9
#
(X UTM B − X UTM A )2 + (YUTM B − YUTM A ) 2
"CA.
@
( D Av )UTM ( D AB )UTM ( DBV )UTM = = senB senV senAˆ
( D VA )UTM = ( DBV )UTM =
senBˆ ( D AB )UTM senV
senA B ( D A )UTM senV 56
%
-67 . /67 0
+
A
!
@
"@ " 5A@
(∆ x VA )UTM = ( D VA )UTM ⋅ senO VA ∆ y VA )UTM = ( D VA )UTM ⋅ cos O VA ( X V )UTM = ( X A )UTM + (∆ x VA )UTM (YV )UTM = (Y A )UTM + (∆ y VA )UTM
$1
!0
+
C@
(∆ x VB )UTM = ( DBV )UTM ⋅ senOBV (∆ y VB )UTM = ( DBV ) TM ⋅ cos OBV ( X V )UTM = ( X B )UTM + (∆ x VB )UTM (YV )UTM = (YB )UTM + (∆ y VB )UTM %
:
!
"5
C8
= %
'
! : !
%
(
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!
:
(
DG2 =
: . 5
!
(
%
9
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2 DUTM h h 1 + 1 1 + 2 + ∆h 2 2 k R R
!
+ #
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DG2 = ∆h 2 + Dr2
R8
Dr = DG2 − ∆h 2 "
!
" 5C.
#
#
v
B
#
@
V
Dr A D D = rA = rB senB senV senAˆ
V
Dr A = V
Dr B =
senBˆ B Dr A senV
senA B Dr A senV
$3
%
A
!
#
(HV ) A ⋅ HV =
-
(
5
-
(
. )
1 1 + (HV ) B ⋅ V V DA DB 1 1 + V V D A DB
= + 5
9 +
"5
:
;
! + 5+ 9
(
!
9 . 5 # 9
# !
. .$ 5& !
# . . $ 5& # * 51 "+ + 5C+ +
!
2
! GG
! +
<
#
" 5 C.
A
# .5
5
8
5
#
8
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9
#
+ "C. + + ". C+ + / "C+
→
AP1 AB = sen 1 sen B
"+ +
→
AP1 PP = 1 2 sen 3 sen 5
#
C+ +
→
BP2 PP = 1 2 sen 2 sen 6
9
#
C+ "
→
BP2 AB = sen A sen 4
9
@
9
#
"C+
9
#
9
!
@
AB sen 1 = AP1 sen B AP1 sen 3 = P1 P2 sen 5 P1 P2 sen 6 = BP2 sen 2 P2 B sen A = AB sen 4 . . $.
5 '
: 1
. $. &.
#
*
@
AB ⋅ AP1 ⋅ P1 P2 ⋅ P2 B sen 1 ⋅ sen 3 ⋅ sen 6 ⋅ sen A = AP1 ⋅ P1 P2 ⋅ P2 B ⋅ AB sen B ⋅ sen 5 ⋅ sen 2 ⋅ sen 4 sen B sen 1 ⋅ sen 3 ⋅ sen 6 = =E sen A sen 5 ⋅ sen 2 ⋅ sen 4 7
A+ B = 2+3
senB =E senA %
2
5$@
2+3 = H /
@
A + B = H = 2+3 → B = H-A $J
senB = E → sen(H - A) = E ⋅ senA senA senH ⋅ cosA - cosH ⋅ senA = E ⋅ senA senH ⋅ cosA = (senA) ⋅ (E + cosH) tg A =
sen H E + cos H
B=H−A 9
!
(
8 :
)
# : .
:
: 5
.
#
8 '
P1 A =
AB ⋅ sen B sen 1
P1 B =
AB ⋅ sen(A + 5) sen 1
P2 A =
AB ⋅ sen(B + 6) sen 4
P2 B =
AB ⋅ sen A sen 4
θ AP1 = θ BA + A + 5
&G
θ AP2 = θ BA + A θ BP1 = θ BA − B θ BP1 = θ BA − B − 6 5 + 5+
!
=
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!
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9
#
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BP1 AB = sen α 1 sen A 9
#
C+ + @
BP1 BP2 = sen α 2 senβ 1 9
#
C+ +$@
BP3 BP2 = sen α 3 senβ 2 9
#
C+$ @
BP3 BC = sen C senβ 3 !
@
AB ⋅ BP1 ⋅ BP2 ⋅ BP3 BP1 ⋅ BP2 ⋅ BP3 BC = senα 1 ⋅ senα 2 ⋅ senα 3 senC senA ⋅ senβ1 ⋅ senβ 2 ⋅ senβ 3
AB BC = senα 1 ⋅ senα 2 ⋅ senα 3 senC senA ⋅ senβ 1 ⋅ senβ 2 ⋅ senβ 3 senA BC ⋅ senα 1 ⋅ senα 2 ⋅ senα 3 = =M senC AB ⋅ senβ1 ⋅ senβ 2 ⋅ senβ 3 +
#
'
@
A + C = (n − 2) ⋅ 200 − (α 1 + α 2 + α 3 + β 1 + β 2 + β 3 + B) A+C = N sen A =M sen C A+C = N
(sen(N − A)) ⋅ M = sen A
(sen N ⋅ cos A − cos N ⋅ sen A) ⋅ M = sen A tgA =
senN 1
M
+ cos N
&
C=N−A :
+
5
;
!
:
#
! 5
5
8
@
D PA1 = D BA
sen(200 − A − α 1 ) sen α 1
D BP1 = D AB
sen A senα 1
θ Ap1 = θ BA + A θ BP1 = θ BA − (200 − A − α 1 )
D BP3 = D CB
D CP3 = D CB
sen C sen β 3
sen(200 − C − β 3 ) sen β 3
θ BP3 = θ CB + (200 − C − β 3 ) θ CP3 = θ CB − C
D BP2 = D BP1
sen β 1 sen α 2
D BP2 = D BP3
sen α 3 sen β 2
θ BP 2 = θ BC + (200 − C − β 3 ) + (200 − α 3 − β 2 ) ( 5 !
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