有關Law of sines的問題

like upstair,(180-C1)
[I am explaining it]
you know sine is in a triangle (e.g 3^2 + 4^2 = 5^2)

now you draw an labled x&y axis and a 3,4,5triangle
on the +x,+y(quadrant1)the angle (4,3)=A (0,0)=B
(4,0)=C
and sine = AB/AC = 3/5
\ and / = hypotenuse:
Flip the triangle over y-axis to +x,-y(quadrant 2)
Y
A1\ | /A
\ | /
C1 B1\|/B C
----------------------X
but stil the triangle is = AB/AC,and AB,AC are
postive and all the value are the same
if angle ABC is 28.6, the angle ofA1B1C= 180-ABC
notA!B!C!(counting from 0)
so they got the same number with 180-C

hope can help you

2009-01-29 09:39:03 補充：
Y
A1\ | /A
\ | /
C1 B1\|/B C

2009-01-29 09:39:42 補充：
--------Y
---A1\ | /A
-------\ | /
C1 B1\|/B C

2009-01-29 09:40:24 補充：
---------Y
----A1\ | /A
--------\ | /
C1 B1\|/B C
---------------------->X

sin C = sin (180 - C )
so there are two possibilties
sin C = （7sin20）/5 or sin (180 - C) =（7sin20）/5
C = 28.6 or 151.4