The picture shows a cement bag of weight Fg hanging from a rope which itself is supported by two other ropes attached to a ceiling. The latter two ropes make an angle θ1 and θ2 with the ceiling. Determine the tension in each rope. Use the angle addition identity to simplify your result: sin(α ± β) = sin α cos β ± cos α sin β

Step-by-step explanation:

From the free body diagram attached  below; we will see that

T₃ = Fg   ------ (1)

Thus; as the system is in equilibrium, the net force in the x and y direction shows to be zero

Then;

Also;

  ---- (3)

From equation (2):

Replacing the above value for  T₂  into equation 3; we have

 ---- (4)

Using trigonometric identity Sin (A+B) = SIn A cos B + Cos A sin B

So ; equation 4 can now be:

 --- (5)

replacing equation (1) into  equation (5) ; we have:

Hence; the tension in the string is: