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The image you have shared includes a physics problem involving forces in equilibrium, specifically related to an anchoring system for a climber. From what I can see, the problem involves calculating the forces acting on each anchorage point.

### Given information:
- The weight of the climber \( F_g = 490 \, \text{N} \).
- Two anchorage points are symmetrically placed at an angle of \( 30^\circ \) from the vertical (as shown in the diagram).
- The forces in question are represented as the sum of the forces applied to each anchor (represented in blue).
- The goal is to determine the resultant force exerted on each anchorage.

### Step-by-step approach:

The climber's weight \( F_g = 490 \, \text{N} \) acts vertically downward, and this force is distributed between the two anchoring points symmetrically.

#### 1. Symmetry in the problem:
The system is symmetrical, with both anchorages experiencing the same force due to the equal distribution of weight. Each anchor is at an angle of \( 30^\circ \) from the vertical.

#### 2. Vertical force equilibrium:
The vertical component of the forces from both anchors must add up to balance the climber's weight:
\[
F_{1y} + F_{2y} = F_g
\]
Since the forces are symmetrical:
\[
2 F_y = F_g
\]

#### 3. Force components:
Each force \( F \) from an anchor can be split into vertical and horizontal components. The vertical component is:
\[
F_y = F \cos(30^\circ)
\]

Thus:
\[
2 F \cos(30^\circ) = F_g
\]
\[
F = \frac{F_g}{2 \cos(30^\circ)}
\]
\[
F = \frac{490 \, \text{N}}{2 \times 0.866}
\]
\[
F = \frac{490}{1.732}
\]
\[
F \approx 282.85 \, \text{N}
\]

So, the force exerted on each anchorage point is approximately \( 282.85 \, \text{N} \).

Would you like a more detailed explanation or clarification on any part of this solution? Here are five related questions you might find helpful:

1. How would the force distribution change if the angles were not symmetric?
2. What is the horizontal component of the force on each anchor?
3. How would the result change if the weight of the climber was different?
4. What if there were more than two anchorage points? How would the forces be distributed?
5. How does the angle of the anchorage points affect the tension in the rope?

### Tip:
In problems involving equilibrium and angles, always consider splitting forces into their horizontal and vertical components to simplify the calculations.

Determine the resultant force exerted on each anchorage point, given a climber's weight of 490 N distributed symmetrically between two anchorage points at a 30° angle.

This problem involves calculating the resultant force exerted on two symmetrically placed anchorage points at 30° angles, balancing a climber's weight of 490 N. Learn how trigonometry and equilibrium principles apply.

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