Write expressions for the x- and y-components of the cables in terms of the angles. Using the labels "A" and "B" for the tension on the cables, the x-components are Ax = A*cos(a) and Bx = B*cos(b), where a and b are the angles the cables form with respect to the horizontal. The y-components are Ay = A*sin(a) and By = B*sin(b). For example, if a = 30 degrees and b = 45 degrees, the components are:
Ax = A*cos(30) = 0.866*A
Bx = B*cos(45) = 0.707*B
Ay = A*sin(30) = 0.5*A
By = B*sin(45) = 0.707*B
Equate the x-components of A and B, and solve for A. The force exerted by the mass on the cables must be equal in the horizontal directions. For example:
0.866*A = 0.707*B
A = (0.707/0.866)*B
A = 0.816*B
Equate the sum of the y-components to the weight of the mass. The upward tension on the cables equals the downward force exerted by the mass. For example, if the weight of the mass is 60 pounds, 0.5*A + 0.707*B = 60.
Combine the expression by substitution and solve for B. For example:
0.5*(0.816*B) + 0.707*B = 60
0.408*B + 0.707*B = 60
1.114*B = 60
B = 53.8 pounds
Evaluate A by substitution. For example:
A = 0.816*53.8
A = 43.9 pounds