Solving for b to get a

[stang]

So I have these 3 equations:
1) 0 = L1*sin(90-a) + L2*sin(b-90) + L3*sin(90-c)
2) L = L1*cos(90-a) + L2*cos(b-90) + L3*cos(90-c)
3) c = 180 - b + k
For which only angles a, b, and c are unknown, and all the rest are known

So substituting equation 3 into equations 1 and 2, and moving a to the left side, I get:
1) L1*sin(90-a) = -L2*sin(b-90) - L3*sin(b-90-k)
2) L1*cos(90-a) = L - L2*cos(b-90) - L3*cos(b-90-k)

Which I believe can be further reduced to form these 2 equations:
1) L1*cos(a) = L2*cos(b) + L3*cos(b-k)
2) L1*sin(a) = L - L2*sin(b) - L3*sin(b-k)
Using
cos(90-a) = sin(a)
sin(90-a) = cos(a)
cos(b-90) = sin(b)
sin(b-90) = -cos(b)

So now I am at the point where I am trying to rearrange equation 1 to solve for b, so that I can plug that into equation 2 and solve for a. This is where I am stuck.

 

[Otis]

only angles a, b, and c are unknown, and all the rest are known

Please provide all of the known values.

 

[stang]

Please provide all of the known values.

OK...

L1 = 33
L2 = 100
L3 = 125
L = 216.75
k = 65 degrees (but can vary)

 

[stang]

Please provide all of the known values.

Correction: k=-65. I forgot the minus sign! I will correct it in the post itself as soon as it appears here, where I can edit it...