Very hard physics question :D

a 20N crate is suspended by 2 ropes, one with a angle of 40 degrees and the other with a angle of 15 degrees. Find T1 and T2.

This was a extra credit problem and i must know how to solve it! it's bugging me! lol

Zero horizontal force:
T1 sin(40) = T2 sin(15)

Zero vertical force

T1 cos(40) + T2 cos(15) = 20

From these two equations in two unknowns you can easily solve for both.
E.g.

The first equation tells you that

T1 = T2 sin(15)/sin(40)

Substituting this in the second equation gives:

T2 sin(15)/sin(40) * cos(40) + T2 cos(15) = 20

T2 ( sin(15)/tan(40) + cos(15) ) = 20

T2 = 20 / (sin(15)/tan(40) + cos(15))

and then
T1 = 20 (sin(15)/sin(40) ) / ( (sin(15)/tan(40) + cos(15))