To find the angle formed where the X formation meets the top of the table, we can use some trigonometric relationships. Specifically, we can use the cosine function.
Let's denote:
- \( h = 2.5 \) feet (the height of the legs),
- \( d = 5 \) feet (the diagonal distance from the top of one leg to the bottom of the other).
We can visualize this setup as a right triangle where:
- One leg is the height \( h \),
- The other leg is the horizontal distance \( x \) between the two legs at the table's top.
Using the Pythagorean theorem, we can relate the diagonal distance \( d \), height \( h \), and horizontal distance \( x \):
\[ d^2 = h^2 + x^2 \]
Substituting the values we have:
\[ 5^2 = (2.5)^2 + x^2 \] \[ 25 = 6.25 + x^2 \] \[ x^2 = 25 - 6.25 \] \[ x^2 = 18.75 \] \[ x = \sqrt{18.75} \] \[ x \approx 4.33 \text{ feet} \]
Now, we can find the angle \( \theta \) at which the X formation meets the top of the table using the cosine function:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{h}{d} \]
Substituting the known values:
\[ \cos(\theta) = \frac{2.5}{5} = 0.5 \]
Now, we take the inverse cosine to find the angle:
\[ \theta = \cos^{-1}(0.5) \]
The cosine inverse of 0.5 corresponds to:
\[ \theta = 60^\circ \]
Therefore, rounding to the nearest whole degree, the approximate angle formed where the X formation meets the top of the table is:
\[ \boxed{60} \] degrees.