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The problem involves a 300 N ball hanging by two ropes at angles of 60° and 40° from the horizontal. We are tasked with finding the tensions in the ropes labeled \(A\) and \(B\).

### Step-by-Step Solution:

1. **Free Body Diagram**:
   The forces acting on the ball are:
   - The gravitational force, \( W = 300 \, \text{N} \), acting vertically downwards.
   - The tension in rope \( A \), \( T_A \), acting upwards at a 60° angle from the horizontal.
   - The tension in rope \( B \), \( T_B \), acting upwards at a 40° angle from the horizontal.

2. **Equilibrium Conditions**:
   Since the ball is at rest, the system is in equilibrium. We can break this down into two components: 
   - **Vertical equilibrium**: The sum of the vertical components of the tensions in ropes \(A\) and \(B\) must equal the weight of the ball.
   - **Horizontal equilibrium**: The horizontal components of the tensions in ropes \(A\) and \(B\) must cancel each other out.

3. **Setting up the equations**:
   
   - **Horizontal equilibrium**:
     \[
     T_A \cos(60^\circ) = T_B \cos(40^\circ)
     \]
   
   - **Vertical equilibrium**:
     \[
     T_A \sin(60^\circ) + T_B \sin(40^\circ) = 300 \, \text{N}
     \]

### Solving the system of equations:
We have two equations with two unknowns \(T_A\) and \(T_B\). I'll solve these equations for the tensions.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can still explain the process of solving this by hand, or you can upload another request. Let me know how you'd prefer to proceed!

Would you like further details on the method? Here are 5 related questions that might expand your understanding:

1. How do we break forces into components in different directions?
2. Why do we use trigonometric functions in force analysis problems?
3. How do we interpret equilibrium conditions in mechanics?
4. How does the angle of the rope affect the tension in it?
5. What is the significance of solving simultaneous equations in physics?

**Tip:** Always resolve forces into their components when dealing with angled forces in equilibrium problems to simplify the calculations.

Una pelota de 300N cuelga atada a otras dos cuerdas como se observa en la figura. Encuentren las tensiones de las cuerdas A, B y C.

Solve for the tensions in ropes A and B with respective angles of 60° and 40°, supporting a 300N ball. This problem involves trigonometry and static equilibrium equations, ideal for students in Grades 11-12.

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