the faux lab

Solve the 3 problems thusly:

1.  The equal tension "stoplight".

Break the tensions into "vertical" components:  T cos (theta) each, where theta is actually half of the angle you measure.

Solving this:

2 T cos (theta) = W

See how closely the left side of this equation (with your values plugged in) matches the right side.

2.  The unequal tension problem.

Similar to above:

T1 cos (theta 1) + T2 (theta 2) = W

Also:

T1 sin (theta 1) + T2 sin (theta 2)

See how closely the left side of this equation (with your values plugged in) matches the right side.

3.  Using the angle and weight designation from the board (where angles are measured with respect to a "horizontal" axis, it should be true that:

"Lefts" equal "rights"

W1 cos (theta 1) + W3 cos (theta 3) = W2 cos (theta 2) + W4 cos (theta 4)

and

"ups" = "downs"

W1 sin (theta 1) + W2 sin (theta 2) = W3 sin (theta 3) + W4 sin (theta 4)

Pictures forthcoming.