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T R
G
o
N O M E T R
~
Tbe Solulion of Ihe Car•• of oblique rpherie. l Tria.gles,
(ihid.
n~
4.•nd 5.)
C.reI
Gi.eDI
Soughl
I
Solulion
¡
Two fides
AC,
BC'l The angle B OP·, '""A's- fi-"n-e-;'B"C"-:
G"'n-e-A~:-:7G-De--'A'""C"-:"'ü-o-e-:-:iH
and .n .ogle A oppo
poG,e
10
,he .
(by ,heor. , .) Note, ,his
e.reis
ambi·
1
fite ' o one nf Ihem.
I
olher
I
guous 'when BC il leEs ,han AC; Gnee
I
i[
caonot be determioed from (he: data
whclher B be
aCUle
or
obture.
r.volides
AC.
BC,
•nd
.0
.ogle A oppo,
Gte
tO
one of thcm.
fhe Includ<d
I
Upon A!:l
produee~0f
nced be) lel f.1I
.ogle ACB
Ihe perpendieularCD : ,heo (by Iheor.
\
4' ) "d . ':
eo.fioe AC :: lang. A: eo·
,.ng. ACD ; bOl (by lheor.
1.)
,".og.
BC : lang . AC :: eo.fioe ACD : co.
I
fine BCD. Whedee ACB=ACD:±:
BCD is known;
and
.0
.o¡tle oppofite
AB
AD (by ,heor.
1. )
and (by lheor.
2.)
I
T",o Gdes AC. BC, / The o,her fidéo
I
As rad. :
eo.un·
e~'""A:-::-,-a-n-g-. '""A'""C~'-:-,-.n-g-.I
3
AD : eo· Goe RD. No,e, lhis and Ihe
I
lO
one ofthem
I
AS
co-fine..AC : co·fine
Be::
co.fine
i
1.(1
eare are bo,h ambiguou. wheo lhe
~r(l
is fo .
4
Two fideo AC. AH,
.od Ihe iocluded
.ngle A
Tbe olher lide
-1
As ,.d. : eo.6ne A : : tango AC : lan.
BC
AB (by lheor.
1.)
whenee AD is .Ifo
1
kno,"n : ,hen (by lheor.
2.)
.s eo.fine
AD : co.fine HD : : co·fioe AC : eo.
fine BC.
---I)"'T=-w-o-a-n-g"'le-s-A-,-."'B-, -.n-d-:-!-l -'T=h-e--;6~d'e-B=C:-o-p--I
As
fiOl
B : fi ne AC :: 'fin< A: lioe BC
8
• lide AC oppofi,e.
pofi.. Ihe o,her
I
(by ,heorem
l .)
10
one of ,hem
I
• 'lide AC oppofi..
belwixl lhom
AD (by ,heor , ) and . s : ,.ng B:
I
Two .ngre. A,B. aod
The(,de
AB
I
As ·r..d . : eo.Gne A :: taog . AC : tan·
9
10
o.e of Ibem
taog. A :: fioe AD : fine BD (by
,heor. 4') whence AB il alfo known.
--
Two ¡nglta A,B, and
The
other angle . As rad : co·fine AC
::
u ng. A: co-::
a 6de AC oppofile lo
ACB
ung. ACD (by lheor. 4' ) .nd as eo-
10
ooe of Ihem
fine A : eo·Gne n :: une ACD : fine
BCD (by ,heor. 3.) whence ACn is
_.____ ,_ ________.!....______
...l-.:..I_fo:..;.:k~:o.::w.:.:n.:.·
__________
1
VelL .
lI!. N° 98•
8 R
t
c.ro