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The problem shown in the image requires us to determine the magnitudes of \(F_1\) and \(F_2\) for equilibrium, given \( \theta = 60^\circ \) and \( F_2 = 6 \text{ kN} \).

### Approach:
To achieve equilibrium at joint \(O\), both the sum of the horizontal components and the sum of the vertical components of the forces must be zero.

Given:
- \( \theta = 60^\circ \)
- \( F_2 = 6 \text{ kN} \)

### Force Components:
**For \(F_2\) (70° from -x-axis):**
- \( F_{2x} = F_2 \cos(70^\circ) = 6 \cos(70^\circ) \)
- \( F_{2y} = F_2 \sin(70^\circ) = 6 \sin(70^\circ) \)

**For \(F_1\) (unknown \(\theta\), but let's assume it makes \(\theta\) with the -x-axis since it's symmetry with \(F_2\)):**
- \( F_{1x} = F_1 \cos(\theta) \)
- \( F_{1y} = F_1 \sin(\theta) \)

### Equilibrium Equations:
1. **Horizontal equilibrium (\(\Sigma F_x = 0\)):**
   \[
   F_{1x} + F_{2x} = 0
   \]
   \[
   F_1 \cos(\theta) + 6 \cos(70^\circ) = 0
   \]

2. **Vertical equilibrium (\(\Sigma F_y = 0\)):**
   \[
   F_{1y} + F_{2y} = 0
   \]
   \[
   F_1 \sin(\theta) + 6 \sin(70^\circ) = 0
   \]

### Solving for \( F_1 \):
Since \( \theta = 60^\circ \):
- \( F_1 \cos(60^\circ) + 6 \cos(70^\circ) = 0 \)
- \( F_1 \sin(60^\circ) + 6 \sin(70^\circ) = 0 \)

Let's compute \( F_1 \) using these equations.The magnitude of \( F_1 \) required for equilibrium is approximately \( 4.10 \) kN, with its components being \(-2.05\) kN in the x-direction and \(-5.64\) kN in the y-direction.

### Summary:
- \( F_1 \approx 4.10 \) kN
- Components of \( F_1 \): \( F_{1x} \approx -2.05 \) kN, \( F_{1y} \approx -5.64 \) kN
- \( F_2 \) is given as \( 6 \) kN at an angle of \( 70^\circ \) to the negative x-axis.

Would you like more details on this or have any further questions?

### Related Questions:
1. How does changing the angle \( \theta \) affect the magnitude of \( F_1 \)?
2. What would the force components be if \( \theta \) were set to a different value?
3. How does the principle of superposition apply to this problem?
4. What would happen if additional forces were added to the truss?
5. How can this equilibrium condition be verified experimentally?

### Tip:
When verifying the results, it's useful to check that the sum of the x-components and y-components of the forces indeed results in zero, confirming the state of equilibrium.

The members of a truss are pin connected at joint O. Determine the magnitudes of F1 and F2 for equilibrium. Set θ = 60°. Set F2 = 6 kN.

Solve for the magnitudes of F1 and F2 in a truss system where the members are pin-connected at joint O, given θ = 60°. This statics problem involves trigonometry and equilibrium of forces. Set F2 = 6 kN.

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