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To solve the problem of determining the forces in each member of the truss, we'll use the method of joints. The method involves analyzing the equilibrium of forces at each joint. Here's the step-by-step solution:

### Step 1: Identify the geometry and forces
Given:
- \( F = 800 \, \text{N} \) (downward force at point B)
- Distance \( AB = 3.66 \, \text{m} \)
- Distance \( AC = 2.20 \, \text{m} \)

### Step 2: Calculate angles
Using the given distances, we can calculate the angle at joint \( A \).

\[
\text{tan}(\theta) = \frac{AC}{AB} = \frac{2.20}{3.66}
\]

\[
\theta = \text{tan}^{-1}\left(\frac{2.20}{3.66}\right)
\]

### Step 3: Equilibrium at Joint B
At joint \( B \), we have two forces:
- Force in member \( AB \) (Tension or Compression)
- Force in member \( BC \) (Tension or Compression)
- The external load \( F \) (800 N downward)

The sum of forces in the horizontal and vertical directions must be zero.

#### Vertical Equilibrium at B:
\[
F_{BC} = F = 800 \, \text{N}
\]

Since \( F_{BC} \) is balancing the external downward force, it is in **tension**.

#### Horizontal Equilibrium at B:
\[
F_{AB} = F_{BC} \cdot \text{cos}(\theta)
\]

\( F_{AB} \) can then be calculated, and since it is directed from B to A, it is also in **tension**.

### Step 4: Equilibrium at Joint A
At joint \( A \), we have:
- Vertical reaction at \( A_y \)
- Horizontal reaction at \( A_x \)
- Force in member \( AB \) and \( AC \)

Using the vertical and horizontal equilibrium equations, you can determine these forces as well. But generally, in such simple trusses, the reaction forces at the supports will compensate for any imbalance due to external loads.

### Conclusion:
- \( F_{BC} = 800 \, \text{N} \) (Tension)
- \( F_{AB} \) is calculated based on the angle and is in tension.
- \( F_{AC} \) needs to be determined by considering the vertical and horizontal components, but it will typically be in **compression** as it resists the vertical load.

Would you like a detailed calculation for each step, or do you have any specific questions?

### Related Questions:
1. How do you calculate the angle \( \theta \) precisely?
2. What is the reaction force at joint \( C \)?
3. How does changing the external load \( F \) affect the forces in each member?
4. What happens if the load is applied at point A instead of B?
5. How would the forces change if the truss was inverted (i.e., a flipped configuration)?

### Tip:
When analyzing trusses, always start by breaking down the problem using the method of joints or method of sections, focusing on equilibrium conditions for each joint.

The truss supports a single concentrated load of F = 800 N. Determine the magnitude of the force being transmitted through each member and identify whether it is compression or tension. Dimensions: AB = 3.66 m, AC = 2.20 m.

This truss analysis problem involves determining the forces in each member of a truss subjected to a concentrated load of 800 N at point B. The problem uses the method of joints and equilibrium equations to solve for tension and compression forces in the members. Detailed steps include calculating angles using trigonometry and applying equilibrium conditions.

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