A 184 N bird feeder is supported by three cables. angle 1 is 60 degrees and angle 2 is 30 degrees Find the tension in each cable.

To find the tension in each cable, we can utilize the concept of vector resolution. Let's go step by step to solve the problem:

1. Identify the forces acting on the bird feeder:
- The weight of the bird feeder acts vertically downward and has a magnitude of 184 N.
- The tension in each cable pulls upward to balance the weight.

2. Resolve the weight of the bird feeder into horizontal and vertical components:
- The vertical component of the weight is given by W_vert = W * sin(angle), where W is the weight and angle is the angle between the weight vector and the vertical axis.
- The horizontal component of the weight is given by W_horiz = W * cos(angle).

3. Calculate the tension in each cable using vector resolution:
- Considering the forces acting on the bird feeder, let's label the tensions in the cables as T1, T2, and T3, where T1 is opposite to angle 1, T2 is opposite to angle 2, and T3 is the remaining cable.
- For vertical equilibrium, the sum of the vertical components of the tensions should equal the vertical component of the weight:
T1 * sin(angle1) + T2 * sin(angle2) + T3 = W_vert
- For horizontal equilibrium, the sum of the horizontal components of the tensions should equal the horizontal component of the weight:
T1 * cos(angle1) + T2 * cos(angle2) = W_horiz

4. Substitute the given values into the equations and solve for T1, T2, and T3:
- Vertical equilibrium equation: T1 * sin(60°) + T2 * sin(30°) + T3 = 184 * sin(90°)
- Horizontal equilibrium equation: T1 * cos(60°) + T2 * cos(30°) = 184 * cos(90°)

Using the equations above, you can solve for the tensions in each cable T1, T2, and T3 by substituting the values of the angles and applying trigonometric functions.