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The image contains a geometric problem involving a right triangle. Here’s a transcription of the problem:

**Problem Statement (translated to English):**
"The figure represents a crane that supports a load at point B. The rope AB, which holds the load, can withstand a maximum tension of 900 kg. The length of the horizontal projection BC is 3 meters, and the vertical projection AC is 4 meters. What is the maximum weight that can be supported at point B?"

**Given:**
- The horizontal distance \(BC = 3 \, \text{meters}\)
- The vertical distance \(AC = 4 \, \text{meters}\)
- Maximum tension in rope \(AB = 900 \, \text{kg}\)

**To Find:**
- The maximum weight (in kg) that can be supported at point B.

### Steps to Solve:

1. **Determine the length of the rope \(AB\):**
   Since this is a right triangle, we can use the Pythagorean theorem to find the length of the rope \(AB\).

   \[
   AB = \sqrt{AC^2 + BC^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \, \text{meters}
   \]

2. **Determine the angle \( \theta \) of the rope \(AB\):**
   The angle \( \theta \) between the rope \(AB\) and the vertical line \(AC\) can be found using trigonometry:
   
   \[
   \sin \theta = \frac{BC}{AB} = \frac{3}{5}
   \]

   Thus,
   \[
   \theta = \sin^{-1} \left(\frac{3}{5}\right)
   \]

3. **Calculate the vertical component of the tension:**
   The tension in the rope has a vertical component that supports the weight of the load at point B. The vertical component of the tension is given by:

   \[
   T_{\text{vertical}} = T_{\text{max}} \cdot \cos \theta = 900 \cdot \frac{4}{5} = 720 \, \text{kg}
   \]

   Therefore, the maximum weight that can be supported at point B is 720 kg.

### Final Answer:
The maximum weight that can be supported at point B is **720 kg**.

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Would you like further details or have any questions about this solution?

### Related Questions:
1. How do you find the horizontal component of the tension in the rope?
2. What happens to the maximum weight if the rope's maximum tension is increased?
3. Can you calculate the angle between the rope and the horizontal line BC?
4. What is the relationship between the tension in the rope and the weight supported at point B?
5. How would the problem change if the distances AC and BC were altered?

### Tip:
When solving problems involving right triangles, always double-check which trigonometric functions to use for calculating angles and side lengths relative to the triangle's sides.

The figure shows a crane holding a load at point B. The rope AB, which holds the load, can support a maximum tension of 900 kg. The length of the horizontal projection BC is 3 meters, and the vertical projection AC is 4 meters. What is the maximum weight that can be supported at point B?

This problem explores how to calculate the maximum weight supported by a crane using trigonometric concepts and the Pythagorean theorem. It involves analyzing the tension in a right triangle configuration where the crane's rope can support a maximum tension of 900 kg. Ideal for Grades 10-12.

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