Question 1190079
Here's how to solve this problem:

1. **Visualize:** Imagine the semi-ellipse as a horizontal slice of a full ellipse. The two people are standing at the foci (F1 and F2). The distance from a focus to the nearest end of the semi-ellipse is given as 3m. The distance between the foci (2c) is 14m.

2. **Find 'c':** The distance from the center of the ellipse to each focus is 'c'. Since the foci are 14m apart, 2c = 14m, so c = 7m.

3. **Find 'a':** The distance from the center to the end of the semi-ellipse along the major axis is 'a'. We know that the distance from a focus to the nearest end is 3m. Since the distance from the center to the focus is 7m, we have:

   a = c + 3m = 7m + 3m = 10m

4. **Find 'b':**  'b' is the distance from the center to the highest point of the semi-ellipse (the height of the dome at the center). We use the relationship for ellipses:

   a² = b² + c²

   10² = b² + 7²

   100 = b² + 49

   b² = 100 - 49

   b² = 51

   b = √51 ≈ 7.14m

Therefore, the dome is approximately 7.14 meters high at the center.