Tension-conflict between math and physics?

Question

http://img149.imageshack.us/my.php?image=44545464864654se5.gif
I have a conflict between math and physics.
T1 and T2 are strings that go from the ceiling and hold 8 kg.
(Gravity = 10 m/s in this calculations so 8kg=80Newton)
http://img149.imageshack.us/my.php?image...
angle A=60
angle B=53
I used the Law of sines:
so:
t2/sin53 = t1/sin 60
t1=t2*sin60/sin53=1.0842t2
t1=1.0842*t2
--------------------------------------...
but if I take the vectors and find how much each is pulling to the X axis and to the Y axis get that:
t1=t2*cos60/cos53=0.8...
Whats wrong?

why T1*cos60
and not T1*cos53?

Answer 1

I think you have angles incorrectly marked.
So let's do it!
X- components

T1cos(A)=T2 cos(B) or
T1=T2 (cos(B)/cos(A))

Y-components
W - T1sin(A) - T2sin(B) = 0

then
W - T2 (cos(B)/cos(A))sin(A) - T2sin(B) = 0

T2= W/(cos(B) tan(A) + sin(B))
T2= 8 x 9.81/( cos(53) tan(60) + sin(53))
T2= 42.6 N
T1=T2 (cos(B)/cos(A))
T1=42.6(cos(53)/cos(60))
T1=51.3 N

Have fun my friend.

Answer 2

> t2/sin53 = t1/sin 60

This is wrong, because "T1" and "T2" do NOT represent the lengths of the sides of the triangle! You cannot assume that the sizes of the TENSIONS are in the same ratio as the lengths of the strings; so the law of sines is not applicable.

> but if I take the vectors ...

Your equation got cut off, but the part I can see looks correct.