Now calculate the distance between the pylons, that is, the length of the span of the bridge, correct to one decimal place

To calculate the distance between the pylons, which is the span of the bridge, we can use the Pythagorean theorem. The two straight beams from the tops of the pylons to point \( C \) form two right-angled triangles.

### Given Data:
1. The height of point \( C \) above the top of the pylons: \( 47 \, \text{m} \).
2. The horizontal distance from one pylon to point \( C \): \( 65 \, \text{m} \).

### Steps to Calculate the Span of the Bridge:
1. **Consider the right triangle:**
   - The vertical side (opposite side) is the height difference between point \( C \) and the top of the pylon, which is \( 47 \, \text{m} \).
   - The horizontal side (adjacent side) is the distance from the pylon to point \( C \), which is \( 65 \, \text{m} \).

2. **Use the Pythagorean theorem:**
   The hypotenuse \( h \) is the length of the beam connecting the pylon to point \( C \), and can be found as:
   \[
   h = \sqrt{(65 \, \text{m})^2 + (47 \, \text{m})^2}
   \]

3. **Calculate the distance between the pylons:**
   Since there are two such beams meeting at point \( C \), the span of the bridge is twice the horizontal distance from the pylon to point \( C \), which is:
   \[
   \text{Span} = 2 \times 65 \, \text{m} = 130 \, \text{m}
   \]

Thus, the distance between the pylons, or the span of the bridge, is **130.0 meters** (correct to one decimal place).

Would you like more details or have any questions? Here are some related questions that could help deepen your understanding:

1. How does the height difference of \( 47 \, \text{m} \) impact the tension in the beams?
2. What is the total length of the beams used in the bridge structure?
3. How would the span change if the height difference between \( C \) and the pylons was altered?
4. How could we calculate the forces exerted on the pylons due to the bridge's structure?
5. What other methods could be used to calculate the span of a bridge?

**Tip:** When working with right triangles, always check if you can apply the Pythagorean theorem for straightforward calculations of distances and lengths.

Learn how to calculate the distance between bridge pylons, also known as the span of the bridge, using the Pythagorean theorem. Includes a detailed explanation with given data, formulas, and step-by-step calculations. Suitable for Grades 7-9 students.

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